It's tradition. I'm not exactly sure where the tradition comes from, but there is a series of traditional prime lenses for 35mm, and these are still carried on in prime lenses today, and in less likely places: zoom-reflector flashes tend to zoom in a series of big steps matching these focal lengths, and one often finds the same thing with compact camera zooms (lower-end Canon P&S cameras often show this dramatically, with only half a dozen stops, each at roughly one of these marks).
- 100mm / 105mm
With the exception of 28mm and 85mm, these roughly follow a sequence on the order of the square root of two, which I don't think is for any magical reason except that it's a decent enough spacing and because hey, we're familiar with that math in photography. As Stan notes in a comment, the starting point in this little sequence is almost certainly 50mm, chosen for convenience as a readily-available existing cinematography lens design when the 35mm film format was invented.
I put the focal lengths in the root-2 sequence in bold; I also put 70mm in italics because despite being in the sequence, for some reason it's a more rare duck in actual prime lenses (but it's still common for flash zoom steps).
These steps tend to be the end of zoom focal length ranges as well. For example, 24-70mm, 70-200mm, and 24-105mm are all common, and we could argue that 16-35mm (Canon) or 18-35mm (Sigma) fits the pattern well enough too.
Note that focal length numbers are often rounded to a "nice" number, except at the wider end where a single mm makes a big difference in angle of view; it's often the case that the lens's actual focal length is different from the nominal one, but we still call it, for example, a 35mm lens.
There are also notable lenses that aren't in the above list.
My dad's old Minolta came with a 55mm "normal" lens, and Pentax makes a 55mm portrait lens today. Or, there is a popular basic lens design for a very low-profile ("pancake") 40mm lens, available in different designs from Pentax, Voigtlander, and Canon today and in older versions from Nikon and Konica and probably others.
Macro lenses are often 60mm or 90mm. (For whatever reason, SLR primes of these lengths are rarely not macro designs; there may be some appeal in making macro lens not exactly coincide with the focal lengths of lenses people already have? That's speculation.)
And, of course, because they can't resist being odd, Pentax's FA Limited series is 31mm, 43mm, and 77mm. (43mm matching the diagonal of a 35mm film frame, 31mm being sqrt(2) down from that, and 77mm because.... I don't know, but it's a lovely lens.)