vpsdime is crazy cheap...

$2/month is enticing, but 128mb ram seems impossible. even 256mb is pushing it.

Debian minimal, with NGINX or some other light HTTP is easy on even 64 megs. On 128, you can do stuff like PHP and you can run whatever efficient web stuff you like. The web is light, if you're efficient about it.

As an aside, one of my friends has a 100 meg free VPS from one of the terrible free vps providers. He has managed to squeeze a Minecraft server on, and that can hold about 2 or 3 players! (apart from the terrible network, cpu and uptime)

You can run a mostly static site on 64.

It isn't (I have one, a whole $15/year due to some ridiculous sale some months ago). Consider that it's userspace only, so kernel doesn't count. I'm running a (light-duty) nodejs app, nginx to proxy it, tmux, and two irssi instances on mine right now, with memory to spare. Light PHP works fine too (haven't tried anything heavier).

A database server or similar wouldn't work, of course.

If you pay $2/month, you're a sucker; they've got lots of coupons (like the seemingly permanent 25 % discount on their website. If you look a bit further, you'll find even better discounts).