I'll call this a hack because I'm going to use one program to change another in a way not intended by the author.
I've read guides on how to increase the memory usage of minecraft and they were complicated as hell, so here is my simple solution: Use MC Patcher to increase the ram minecraft uses. This works even if you don't or can't use HD textures.
This only works if you have enough ram.
1) As always: backup your minecraft.jar you'll find it in C:\Users\[Your User Name]\AppData\Roaming\.minecraft\bin\ The easiest way is to just copy and paste a new one. Windows will rename it minecraft - copy.jar automatically. If you need to change back just delete your minecraft.jar and remove the " - copy" from your backup.
2) Download MC patcher
3) Run it.
4) Click the "options" tab
5) In the "Java heap size (MB)" enter the amount of ram you want minecraft to use. 1 gig = 1024 MB, here I entered 2048 which is 2 gigs
6) Click the Mods tab and click patch.
If your computer is up to it you can now run HD textures but even if it isn't you've just increased the amount of ram minecraft will use which will speed it up - a lot!