TL;DR answer
In general, Canon DSLRs require a maximum aperture of at least f/5.6 to autofocus. Depending on the camera model, and with some exceptions, a maximum aperture of at least f/2.8 or f/4 enables cross-type and/or high-precision focusing. EOS-1 series cameras and the EOS 5D Mark III (with the latest firmware) can autofocus at f/8, but only with the center point.
Definitions
- A horizontal-sensitive point or vertical-sensitive point is an autofocus point that can detect horizontal or vertical lines, respectively. A horizontal-sensitive point cannot detect vertical lines, and a vertical-sensitive point cannot detect horizontal lines.
- A high-precision sensor is an autofocus sensor that is capable of focusing within 1/3 of the depth of field of the lens, instead of simply within the depth of field. These sensors require faster maximum apertures, typically at least f/2.8, in order for them to work.
- A cross-type point is an autofocus point that can detect both horizontal and vertical lines simultaneously. Depending on the camera model, the maximum aperture may need to be at least f/2.8 or f/4 for a point to be cross-type, because the vertical-sensitive part of the AF point is a high-precision sensor.
- A dual cross-type point is an autofocus point that can detect diagonal lines as well as horizontal and vertical lines. The diagonal sensors require at least f/2.8 in order to function because they are high-precision sensors.
Important notes
Where "autofocus does not function" is noted, phase-detection autofocus is normally impossible, either when shooting through the viewfinder or with the Quick AF mode in Live View, but it is generally possible to autofocus using the contrast detection-based Live AF and Face Detection Live AF modes in Live View.
In addition, when an extender (teleconverter) is being used and the resulting aperture is less than what is normally required for AF, it may be possible to enable AF by taping the three extender-specific pins (which are opposite of the raised pins) on the lens side of the extender to prevent it from communicating extender information with the lens and camera, so that the camera sees the lens's aperture as though no extender is attached. This is not guaranteed to succeed as the AF system is not designed to operate under these conditions, and the Exif data will not reflect the use of the extender. Some third-party extenders may not communicate extender information with the lens and camera at all, with the same effect as the aforementioned "tape trick".
The limitations discussed hereafter generally do not apply to third-party zoom lenses that have maximum apertures of f/6.3 at the long end of the zoom range, as they actually report a maximum aperture of f/5.6 to the camera. Note, though, that faster third-party lenses should be able to autofocus as expected for their aperture, including any high-precision focusing capability normally supported by the lens and body.
All images in this answer should be attributed to Canon Inc.
Canon EOS Digital Rebel (original, 300D), Digital Rebel XT (350D), Rebel XS (1000D), Rebel T3 (1100D), D30, D60, 10D
All points function to f/5.6; the center point is normal-precision cross-type (it is both vertical- and horizontal-sensitive to f/5.6 and is not high precision at f/2.8). The other points are either horizontal or vertical sensitive only (not both) (EOS D30 and D60: vertical sensitive only). Autofocus does not function below f/5.6.
- EOS D30 and D60: 3 AF points available.
- EOS 10D, Digital Rebel (300D), Digital Rebel XT (350D), Rebel XS (1000D): 7 AF points available.
- EOS Rebel T3 (1100D): 9 AF points available.
Canon EOS D30/D60 AF array
Canon EOS 1000D AF array
Note that the EOS Rebel T3 (1100D) has essentially the same AF point layout as those in the next group of cameras, only that the center point is not high precision at f/2.8.
Canon EOS Digital Rebel XTi (400D), Rebel XSi (450D), Rebel T1i (500D), Rebel T2i (550D), Rebel T3i (600D), Rebel SL1 (100D), 20D, 30D
The center point is high-precision only when the aperture is at least f/2.8. If below f/2.8 but at least f/5.6, all points function as either horizontal or vertical sensitive only, except for the center point, which functions as standard-precision cross-type. Autofocus does not function below f/5.6.
Canon EOS Rebel T3i (600D) AF array
Canon EOS Rebel T4i (650D), Rebel T5i (700D), 40D, 50D, 60D
The center point is high-precision dual cross-type only when the aperture is at least f/2.8. If below f/2.8 but at least f/5.6, all points function as cross type, but the center point is single cross-type and normal precision only. Autofocus does not function below f/5.6. With the following lenses, the center point is normal-precision single cross-type, as if they were f/5.6 lenses:
- EF 28-80mm f/2.8-4L USM
- EF 50mm f/2.5 Compact Macro
With the following lenses, the outside points of the AF array are either horizontal or vertical sensitive (not both):
- EF 35-80mm f/4-5.6 (all variants)
- EF 35-105mm f/4-5.6 (original and original USM variants only)
- EF 80-200mm f/4.5-5.6 (II and USM variants only)
(EOS Rebel T4i (650D): Though not included in the above link, this limitation is specified in the manual for this camera, page 99.)
Canon EOS 60D AF array
Canon EOS 7D
The same aperture limits for the EOS Rebel T4i (650D), 40D, 50D, and 60D apply to the 7D, only that the 7D has 19 AF points instead of 9.
Canon EOS 7D AF array
Canon EOS 6D
The center point is high-precision cross-type only when the aperture is at least f/2.8; the other points are either horizontal or vertical sensitive (not both). If below f/2.8 but at least f/5.6, the center point remains cross-type but is normal precision only; all other points continue to function normally. Autofocus does not function below f/5.6.
Canon EOS 6D AF array
Canon EOS 5D and EOS 5D Mark II
The center point is high-precision cross-type only when the aperture is at least f/2.8; the other points are either horizontal or vertical sensitive (not both). If below f/2.8 but at least f/5.6, the center point remains cross-type but is normal precision only; all other points continue to function normally. Two of the six invisible Assist AF points used in AI Servo AF are cross-type at f/2.8, with the rest horizontal sensitive; if below f/2.8 but at least f/5.6, they are all horizontal sensitive. Autofocus does not function below f/5.6.
Canon EOS 5D Mark II AF array
Canon EOS-1D, EOS-1Ds, EOS-1D Mark II, EOS-1D Mark II N, EOS-1Ds Mark II
- If at least f/2.8, all 45 autofocus points will function, with 7 points high-precision cross-type.
- If at least f/4, all 45 autofocus points will function, but only the center point is high-precision cross-type.
- If at least f/5.6, all 45 autofocus points will function as horizontal sensitive only.
- If at least f/8, only the center point functions as horizontal sensitive only. The other points will not work.
- Autofocus does not function below f/8.
Note that when using the EF 70-200mm f/2.8L USM lens (without IS) with an Extender, use the center point only as the other points may not focus correctly.
Canon EOS-1D Mark II AF array
Canon EOS-1D Mark III, EOS-1Ds Mark III, EOS-1D Mark IV
- If at least f/2.8, all 45 autofocus points will function, with 19 points high-precision cross-type. (EOS-1D Mark IV only, with manual point selection: 39 of the 45 points are high-precision cross-type.)
Canon EOS-1D Mark III AF array
Canon EOS-1D Mark IV AF array
- If at least f/4, all 45 autofocus points will function, but only the center point is high-precision cross-type.
- If at least f/5.6, all 45 autofocus points will function as horizontal sensitive only.
- If at least f/8, only the center point functions as horizontal sensitive only. The other points will not work.
- Autofocus does not function below f/8.
- There are exceptions:
- All of the AF points will be horizontal sensitive only if a variable-aperture zoom lens is mounted, with the exception of the EF 28-80mm f/2.8-4L USM lens, which allows the center point to work as cross-type.
- EOS-1D Mark III and EOS-1Ds Mark III: When using the EF 70-200mm f/2.8L USM lens (without IS) with an Extender, use the center point only as the other points may not focus correctly.
- The following lenses do not allow the three points on the far left and far right to work as cross-type points (only horizontal sensitive) even though they have a maximum aperture of f/2.8:
- EF 24mm f/2.8
- EF 28mm f/2.8
- EOS-1D Mark IV only: Some lenses and lens/extender combinations enable cross-type focusing with 39 of the 45 points, even though they have a maximum aperture of f/4:
- EF 17-40mm f/4L USM
- EF 24-105mm f/4L IS USM
- EF 70-200mm f/2.8L IS USM with Extender EF 1.4X II
- EF 200mm f/2L IS USM with Extender EF 2X II
- EF 300mm f/2.8L IS USM with Extender EF 1.4X II
- EF 400mm f/2.8L IS USM with Extender EF 1.4X II
Canon EOS 5D Mark III and EOS-1D X
Autofocus capabilities depend on which of the eight groups the lens in use falls into (see the Canon EOS-1D X AF Setting Guidebook, pages 36-39, and Canon EOS 5D Mark III manual, pages 79-84, for more details; a complete and easier-to-navigate list of lenses can be found here), as follows:
Canon EOS-1D X AF array
Group A: Most f/2.8 and faster lenses and lens/extender combinations, with the exception of those listed in Groups B, C, and D, support 41 cross-type points (21 in the center, f/5.6 sensitive, and 10 on each side, f/4 sensitive) and 5 dual cross-type points (in the center column, f/2.8 sensitive). The remaining points are horizontal-sensitive. All 61 AF points and AF area selection modes are available.

Group B: These f/2.8 lenses allow the same functionality as Group A lenses except that only one point is f/2.8 dual cross-type:
- EF 14mm f/2.8L USM
- EF 14mm f/2.8L II USM
- EF 15mm f/2.8 Fisheye
- EF 20mm f/2.8 USM
- EF 24mm f/2.8
- EF 24mm f/2.8 IS USM
- EF 28mm f/2.8 IS USM
- EF 24-70mm f/2.8L USM (original variant only)

Group C: Most f/4 lenses and lens/extender combinations support 41 cross-type points (none of the points are dual cross-type). All 61 AF points and AF area selection modes are available. A few macro lenses are in this group as well:
- EF 50mm f/2.5 Compact Macro
- EF 100mm f/2.8 Macro
- EF 100mm f/2.8L Macro IS USM

Group D: These f/2.8 lenses supports only 31 cross-type points (21 in the center, inner column of 5 on each side) and one f/2.8 dual cross-type point, although all 61 AF points and AF area selection modes are available.
- EF 28mm f/2.8
- EF 40mm f/2.8 STM (pancake lens introduced with EOS Rebel T4i)

Group E: Most f/5.6 lens and lens/extender combinations support 21 cross-type points in the center (none of the side points are cross-type, and there are no dual cross-type points). All 61 AF points and AF area selection modes are available. A few macro lenses are in this group as well:
- EF 50mm f/2.5 Compact Macro with Life-Size Converter EF
- EF 100mm f/2.8 Macro USM

Group F: These lenses support 21 cross-type points in the center, but a total of 47 points are available (seven points from the extremes at each side of the AF array are disabled), although all AF area selection modes are available:
- EF 25-55mm f/4-5.6 USM
- EF 28-70mm f/3.5-4.5 (all variants)
- EF 28-80mm f/3.5-5.6 (all variants)
- EF 28-105mm f/4-5.6 (original and original USM variants only)
- EF 35-70mm f/3.5-4.5 (all variants)
- EF 35-80mm f/4-5.6 (all variants)
- EF 35-350mm f/3.5-5.6L USM
- EF 80-200 f/4-5.6 (II and USM variants only)
- EF 800mm f/5.6L IS USM

Group G: These lenses and lens/extender combinations support 15 cross-type points in the center and a total of 33 points (the top and bottom three cross-type points in the center and 11 points from the extremes at each side of the AF array are disabled), although all AF area selection modes are available:
- EF 180mm f/3.5L Macro USM
- EF 180mm f/3.5L Macro USM with Extender EF 1.4x
- EF 1200mm f/5.6L USM

Group H: EOS-1D X with firmware version 1.1.1 or later, and EOS 5D Mark III with firmware version 1.2.1 or later (see this page): Most f/8 lens/extender combinations, the sole exception being EF 180mm f/3.5L Macro USM with Extender EF 2x (for which autofocus does not function), support autofocus with the center point only, which is cross-type (all other points are disabled). AF point expansion can be used (although only the center point can be selected), with four points adjacent to the center point acting as AF assist points. The points above and below the center point are vertical sensitive, while the points to the left and right of the center point are horizontal sensitive. Autofocus does not function below f/8. This group also includes the following lenses:
- EF 35-105mm f/4.5-5.6
- EF 35-105mm f/4.5-5.6 USM

EOS-1D X with firmware older than version 1.1.1 and EOS 5D Mark III with firmware older than version 1.2.1: Only the center point can be used (all other points are disabled) for the above EF 35-105mm lenses, and AF point expansion is not available. Autofocus does not function below f/5.6.
