Unusual Out of Memory Issues

What I expected to happen was...:
Play with lag-free experience and have fun

What actually happened was...:
Ever since Minecraft 1.6.1, I keep getting Out of Memory crashes

Steps to Reproduce:
1. Open Minecraft
2. Login
3. Go on a multiplayer server or singleplayer
4. Play for a bit
5. Crash

This is a problem because I always run my Minecraft on 1GB of RAM, and recently I've been using the Java flags option in profile on the new launcher and because of these crashes I've been even trying to add a bit more memory and I keep getting out of memory error!

The report the launcher gave me is here. IMPORTANT!
http://pastebin.com/RqRqVJQm