I'm using a 1gb droplet, ubuntu 12.10 with a LEMP stack, PHP5 and MySQL 5 for a low traffic site (Xenforo-based forum) as well. Maybe the difference is nginx vs Apache?

edit: I also added an additional 1gb as swap space, which helped prevent my mysql instance from falling over with low memory at times.

Apache defaults to using prefork on Linux.

Prefork is pretty much Apache-speak for "please munch all my memory and then lock up if more than a handful of people turn up at once".

Nginx or Lighttpd + PHP-FPM behave almost as badly if you choose dynamic mode and don't pick the right values.