There's a few of these sites out there, and browsershots seems to be one of the better.
I'm disapointed at times as some of the browsers they list they really can't check and produce zero results.
Also, if you do decide to run these checks DO NOT click ALL
If you have an older machine, processing ALL on your site can slow your site down. We had a customer contact us a few weeks ago that they ran an ALL scan on a Celeron 1.4 with 512MB ram - it pretty much killed their site for the 30 minutes