So if you mean at what focal lengths are straight lines no longer straight and NOT some kind of perspective distortion, the answer is a bit more complex. Theoretically, it's up to lens design and not focal length dependent. One could imagine a lens design that has no distortion like that at any given focal length. Practically, especially on SLRs, you tend to get more complex distortion at wide focal lengths. But if you can use any lens design you want, you can probably avoid distortion at just about any focal length.
Since this is RFF and I'm more familiar with M lenses, I'll name just a few lenses at different focal lengths which have essentially no distortion:
- Leica 50mm Summicron (current version)
- Zeiss Biogon 35mm f/2
- Leica 28mm f/2.8 Elmarit ASPH
- Zeiss Biogon-C 21mm f/4.5
- Contax G Hologon 16mm f/8
It's generally easier to design telephotos without complex distortion, so there's a bunch at longer focal lengths with relatively little distortion or just mild pincushion distortion.
On the other hand, if you are still talking about perspective distortion, well that's not really a function of focal length, but of camera to subject distance (and viewing distance of the resulting image). It is more evident with wide angle lenses because of their angle of view. Most people don't object to perspective distortion around the 35mm focal length. Some don't like 28mm because it can have a bit too much in close situations, though I find that a focal length that is pretty benign with respect to perspective distortion if limited to 0.7m or more. 24mm and 21mm (and certainly anything wider) can give you perspective distortion pretty easily in most situations.