1. TOS. Does it allow legal adult content. Some of the sites and forums I help set up typically involve the possibility of adult topics talk, or creative writing of fandom/original romance stories that don't stop at kisses so that's the first thing I look at. Probably not what's usually termed porn but sometime not altogether suitable for all publics either, and with a good number of webhosts my visit stops right there, if they explicitly forbid adult content or run on member pages an ad network that does (Goooogle).
2. Appropriate space and bandwidth. But well 95+% of free offers typically have what I'm looking for in a free plan or sometime ridiculously more. I'm usually looking for 200-300 MB space / 3-5 GB bandwidth with reasonable speed and (95+% ?) uptime.
3. Subdomain or even the old "username directory". If I'm forking over for a domain I'll usually go with at least some budget hosting plan. So if it's free it must have one of those.
4. LAMP.
5. Sendmail on. Often find myself setting up forums so the ability to verify addresses, resend passwords or the occasionnal announcement is quite appreciated.
6. FTP that's not overcrowded, phpMyAdmin or some similar solution. If I have that even the most barebones control panel or none at all will do.
7. No weird chmodding or filetype restrictions. I'm fine with forbidden media and music filetypes, but when the filetypes for even such major packages as SMF or myBB give errors because the only one they ever bothered to check was phpbb2, and there's no way to request others that may be needed by less common but still legitimate scripts, time to move on...
8. Ads. The host must obviously have some sort of counterpart. Those I'm usually most at ease with are some sort of self-placed banner or contextual ads on the website part, and a footer linkback on forums. I don't like "compulsory attendance" post4host though I can probably be convinced to post some reasonable initial amount, and I'm usually at least a bit active on forum of hosts I end up really using and like them to be reasonably maintained and friendly.
9. Filesize restriction... I like it to be at least 2 Megs, doesn't really need to be over 5 Megs though. That's, of course, not including the database(s), allowing them to grow as they will within the overall disk space.
10. No spam, thanks. And no third-party surveys.