The owner of Mt. Gox has a web host that accepts bitcoins:
http://www.kalyhost.com/There used to be a web hosting section on this page:
http://en.bitcoin.it/wiki/Trade which you can still find if you access the history. Or do a CTRL+F for "host" and you'll find more suggestions.
Here's another one that hasn't been mentioned yet:
http://www.bitcoinvpshosting.com/Don't let the name fool you. The offer shared hosting plans too. Unless you want to migrate an existing site, then shared hosting is probably best for someone who is just starting out:
http://bitcoinvpshosting.com/bitcoin-shared-hosting/And another one (although their prices are a bit high):
http://blog.rimuhosting.com/2013/12/09/now-accepting-bitcoins/You may want to check Namecheap.com
They accept bitcoin but I don't know if its compulsory to buy a domain with them to host!
If you want free hosting :
www.2freehosting.com is the best
Edit: What do you want to host exactly?
Interesting. I don't think I've seen a web host that
only offers free hosting before. Usually they have multiple tiers and you're expected to upgrade if your website becomes big enough or you get sick of the ads. I wonder how it is that they stay profitable since it's not really mentioned in any detail in the FAQ and they seem to lack ads.
If he was he wouldn't be asking here for any hosting site which accepts Bitcoin
Yeah, that's what I thought as well. A hacker who is probably in control of a large botnet isn't going to be asking this type of question. Unless it's done intentionally to throw people off, I guess.