Depends what you want to do really, and your budget, of course!
If you've already got the PC, that's the expensive bit taken care of - but really you need as much grunt (CPU power) and RAM as you can throw at it - not to mention hard disk space - and speed, if possible.
Those details can be gone into separately.
The other equipment you'll need are;
1. A decent soundcard. Creative Labs make OK ones if you're really tight for cash, but M-Audio packages with outboard input controls and bundled ProTools are outstanding value for money. ProTools is the industry standard software, in case you didn't know Echo are next up the chain, and make superb soundcards for music recording (next to useless for gaming though...), with DigiDesign (makers of ProTools) hardware at the top.
2. Software. If you can't stretch to ProTools, or ProTools lite with an M-Audio package, Sony's ACID is completely brilliant and intuitive - I prefer it to Sonar, which is the next choice - and widely used. Steinberg's Cubase is the other notable - but I find it fiddly and over complex. A great budget choice is Magix Music Studio - at around £50, you can't get cheaper.
3. A mixing desk (for multiple simultaneous inputs). The Spirit Folio is reasonably priced - and pretty good. Tascam do a budget USB job that interfaces with Sonar, so you can control the software from the control knobs with no effort.
4. A keyboard - a MIDI controller keyboard will do, if you're prepared to buy "Soft Synths" and learn how to program the things... or something a bit better with an audio interface would be better.
5. A Line 6 Pod. If you play guitar or know a guitarist, these are indispensable. We use the Pod XT Pro (both bass and guitar versions), and we're still discovering new sounds on them a year down the line. The hardware effects processing saves loads of CPU time too...
6. Microphone. I think it's the SM 58 that's the jack of all trades (someone correct me...).
7. Monitors. Don't bother with computer speakers - you need decent nearfield monitors for your music.
8. Headphones. You don't want feedback from the mic, so use decent Sennheisers. There's no point getting Grados, unless you've got a top-end soundcard and record each instrument using 50 microphones... Headphones are also great for hearing details in the music when you're mixing - and are better for this purpose than the monitors.
9. Luxury extra: Antares. If you've ever sung flat, you need Antares in your studio. As someone with perfect pitch, it's a Godsend.
That's not exhaustive - but I'd guess it's more than a start