I’m a fan of www.nearlyfreespeech.net. They have an extremely simple “pay for what you use” model which is really great for small sites. My site, which I just set up to do programming experiments, post a few pictures on, and share files with my family, literally cost me something like 3 cents per month at the beginning (I’ve since started storing lots and lots of photos there so I’m up to a couple bucks a month in storage fees).
They have a really no-nonsense support team that addresses most issues without the usual tier-1-did-you-plug-it-in runaround, and a system whereby you can set up multiple accounts that can modify a single site. They’re a little leaned towards the “I know what I’m doing and don’t need a lot of hand-holding” crowd, however.
The other feature I like them for is their “funding account” approach. You don’t get a monthly bill or charge on your credit card; you use your credit card to put $5 in an account, and they just deduct money from it in tiny amounts (e.g. 3 cents for my first few months), and send you a warning when it gets down to a certain level. You can put as much or as little in the account as you want, although I think there’s a $5 minimum to open an account. One nice thing about this system is that you can’t suddenly get hit with an enormous bill if your site’s popularity spikes due to a slashdotting or something – it just eats the few dollars you have in the account and temporarily disables the site until you put more money in. Their faq says the average slashdotting costs about 10 bucks to cover without shutting the site down. 
It’s also trivial and free to set up a new site for some temporary purpose. Look, I just created one: http://sdmbexample.nfshost.com