Good recordings start with the sound source. If your instruments sound poor acoustically, they'll sound poor when recorded, so make sure that they're in good working order. If you're a guitarist, have a luthier check the intonation and the guitar's frets to see if any fretwork is required. Also, check input jacks and cables to make sure that they're functioning cleanly; crackles and pops can ruin an otherwise perfect take.
When your instruments are fully functional, tune them. A meticulously arranged and performed song will still sound awful if any of the instruments aren't in tune. Taking the time to check the tuning before and during every session will pay dividends when it comes to listening back to your recordings.
When recording, do everything you can to avoid the digital distortion referred to as "clipping." Make sure that you pay close attention to your pre-fader input levels when recording your signal and adjust the trim level so that the peaks are not exceeding -3dB. Anytime your signals exceed unity gain (0dB), their waveform is literally "clipped" and the signal will distort, so give yourself plenty of headroom.
Try to get the sound you're looking for while tracking, rather than leaving all of your options open for mixdown. Just because digital recording has afforded us the luxury of recording an ungodly number of tracks that can be EQ'd, compressed and edited at the mixdown stage, doesn't mean that we should do it. Sure, it's nice to have options when mixing, but having to sift through multiple vocal and instrumental performances and assemble single tracks from them can be a time-consuming headache. Sometimes, it's more beneficial to work a little harder while tracking in an effort to get better performances and to work on getting a great recorded sound that you can commit to. When you do this, you may find that the mixing session is a lot simpler and less time consuming.
When your tracks are all recorded and it's time to mix, try to be your own harshest critic. Just because you've taken the time to record a slew of tracks for the song doesn't mean that you need them. Listen to all the parts you've recorded and make sure that they're really adding to the song. If they're not, they're just taking up valuable space and robbing you of valuable headroom, so take them out of the mix.
After you've worked on a mix for a couple of hours, take a break and rest your ears. If you work for too long, you may find that your listening skills have diminished somewhat, and when you listen to your mix the next day, you'll often be surprised at how off the mark your judgment was.
When you finally settle on a mix, take it and listen to it on a few different systems. Play it in your car, in your computer, on a portable and on your home stereo system, which should help you address any obvious shortcomings. If you can get your mix to sound pretty good on all of these systems, you know you're on the right track.