A general rule of thumb is that you can shoot handheld with a shutter speed of 1/focal length, with a minimum of 1/60th.
The "speed of at least focal length" rule is traditional for 35mm photography; maybe it works also for larger format on the basis that you are still aiming for the same resolution (lp/mm on the film) and hence more total detail.
But maybe it needs to be updated for DSLR's, for two reasons:
a) smaller sensor means more enlargement and so an image taken with a given focal length will be more blurred by camera movement; that might suggest revising to rule to use the "35mm equivalent focal length".
if your sensor's resolution is significantly more than envisioned in that rule of thumb, due to small pixels, you might want to be more cautious. I suspect that the rule is old enough to be based on only "adequate" rather than excellent resolution, like the "1000 line pairs per picture height" that floats around with depth of field reckoning. So maybe this needs to be adjusted to account for pixel size, which roughly sets the resolution you would like to achieve.
Let me float a version, based on the thinking that DSLR's with sensors 2000 pixels high roughly match the traditionally envisioned sharpness of 35mm film: replace focal length by something like
(focal length in mm)*12/(pixel pitch in microns)
Example: the Nikon D100 has pixel pitch 8 microns, so maximum exposure duration of 1/(1.5*focal length).
This matches tradition for a 35mm format sensor of resolution 2000x3000, because that has pixel pitch of 12 microns, but the actual value of the constant factor 12 is probably something one should adjust personally. That was an experiment we did early in my first photography course: take a sequence of photographs of something with fine detail like writing at various speeds, and examine the slides carefully for sharpness.
I have not heard the "minimum of 1/60" part; would that number apply equally for other formats?