It really depends on what you want to do - there's a multitude of recording options and as such a multitude of budget requirements.
I use a computer and software to record. It's pretty cheap, easy, flexible and can be as quick & dirty or as elaborate as you'd like.
You'll need a couple of things:
1 - obviously a computer. Something at least like a mid range speed computer - nothing old and slow. It doesn't have to be the quickest out there but... A decent amout of RAM also.
2 - software. There's quite a few really good choices out there. I use a Mac, and for that I'd recommend Logic Pro (expensive), Logic Express (much more affordable and still very good), or Garageband (free on current Mac models - very easy to use and quite powerful but lacks pro features). For PC a couple of common ones are Pro Tools, Pro Tools LE (light edition, very good, designed to work with M-Audio interface devices, Cakewalk and lots of others...
3 - Some way of getting audio in and out of your computer. There's lots of options here too - you'll need something that will let you import at least 2 signals via firewire or USB 2, unless you go with a pretty good higher end audio card. Some companies are M-Audio, Digidesigns... there's a lot of options.
4 - decent mics. Your recordings can only be as good as your mics, so get the best quality that you can afford. Some mics are absurdly high priced so you just have to do the best you can.
That's it. This kind of setup can pretty much give you as many tracks as you could possibly want as well as full use of built in effects, compressor, delay, reverb, limiter... It's a pretty good way to go in my opinion.
