This is nothing worse for a miner than hitting lag spikes and fps lows on a older pc. It happens, not everyone who plays Minecraft can afford the latest and greatest or they've been stuck with a laptop sporting an Intel card. Whatever the case may be for those low-end rig blues there is a mod out there that aims at helping to improve your quality time spelunking those canyons. Optifine is a mod for Minecraft supporting all the way up to the recent release of 1.6.4.
This mod typically doubles FPS output and helps to cut down on lag spikes that occur. It also offers a wide array of options to tweak so you can get the most out of your Minecraft experience. From simple settings dealing with view distance and texture quality all the way to being able to turn of particle effects and change how fog and clouds work. You can take your experience down to the base level if need be, it won't be pretty but it will sure fly.
Optifine also offers the option of HD for those with higher-end rigs, this gives you the option to install some insanely awesome looking textures like those below. Of course there won't be any truly nextgen graphics here.
(image courtesy of deviant artist Frozen Dozer)
Installation of Optifine is amazingly simple, all you have to do it download the jar file for your version and run it. This will create a profile on the new Minecraft launcher. It's key to point out you should have already launched that version of the game prior to installing this mod. Check out Optifine here and give it a go.