Hummingbirds perch and rest: capture them then.
(f/6.3, 1/125 sec., ISO 800)
To evaluate the possibility of capturing the birds in flight without a flash, I invite viewers to decide for themselves whether the wings have been adequately frozen in this picture (f/5.6, 1/3200 sec, ISO 800).
In response to a comment, @rfusca has suggested this answer be amplified to point out that exposure duration is not the only determinant of blurriness in motion. The apparent motion of a subject (like a hummingbird's wing) depends on how its velocity is projected onto the sensor. The component of the motion towards and away from the sensor contributes little to the blurring. Moreover, in complex and repetitive motion, like a wingbeat, there often are times when the velocity is relatively small. For example, the first image below was obtained at 1/4000 second and the second image, taken just three seconds later, was obtained at 1/2500 second: almost twice the duration. Yet the second is tack sharp compared to the first for two reasons: (i) almost all its motion is towards the sensor (or away from it--I can't tell which) and (ii) the wing is at a low-speed part of its cycle.