Depending on what you plan on doing with the music after you've converted it determines your best course of action. If you just want it for an MP3 player, any of the direct to hard drive solutions offered above will work. However, if you want to save the music in a "lossless" format vs. MP3's "lossy" format, I would highly recommend Sound Forge software.
Here's a link for a trial version, I'm sure it's been disabled somewhat, but you should be able to get a good feel for the program from the trial version.
Sound Forge trial
As one who's converted 100's of hours of analog music to digital format, and has used this program since version 3.0, I feel it is the best out there for the home user, using a PC.
The bigger issue is how you get the music from your source (album, reel to reel, cassette, video tape, etc) on to your hard drive. Personally, I use a separate sound card, a pre-amp, and an amplifier as I've found it's much easier to tweek the music as it's going in, than to try and adjust it with software after the fact. This is assuming you don't already have a multi-track system, but from your post it sounds like that's not the case.
As has been pointed out, lossless .wav files are BIG, figure about 10 mb per minute of music, so have a lot of real estate available on your storage drive, and if you plan on processing the digital files a fast cpu and plenty of ram help a lot.
It's worth the effort, especially if you have a lot of albums that have not been re-released in a digital format. Frankly, if there is a digital version commercially available, buy it, as you'll never be able to reproduce the nuances from your vinyl compared to what a studio engineer can do from the master tapes.
