I have a number of cameras that do this .. AVC is a native recording format these days.
But seriously, if you’re talking about lower resolution/quality web video, you could by a cheap MP4/AVC camcorder that produces native AVC. A Sanyo Xacti FH-1A will do HD (1080/60p, 1080/60i, 720/30p, 480/30p), for under $300. Some of the fixed focal-length “flip” style camcorders (from Flip, Kodak, others) are slightly more dubious in quality, but run even cheaper. If it’s for a blog or something, that may be all you need.
I know Grass Valley makes some MPEG-4 capture boards… not sure if they’re actually H.264/MPEG-4 Part 10, or only MPEG-4 Part 2, but it might be worth checking out, though not cheap, I expect.
I did a video server project some years back that needed realtime H.264 encoding. At the time I didn’t find anything reasonable for that specific application, though there are a number of boards for security camera operations that do this, if you’re happy with CVBS quality capture. Thing is, they get pricey, since they usually want to take in 8 or more cameras at once.
The solution we used there was software… on a Q6600 processor (my 1U server had two of these), we could get about one SD-ish channel of video encoded into H.264 in an MPEG-2 transport stream per core, using Linux, GStreamer, and x264. But you may not want to dedicate the better part of a PC to this. This guy here did something similar: https://www.wu.ece.ufl.edu/projects/wirelessVideo/project/realTimeCoding/download/doc/howto.pdf
-Dave