1. Properly stretched strings--basically this means that when putting on a new set of strings, you need to tug on the strings to stretch them out. you cannot simply tune the new set up to pitch and expect it to hold--you have to yank on the string and then keep retuning until it no longer goes flat after you yank. i prefer to use an electronic tuner for this--not because my ears stink, but because more often than not i find myself doing the stretching in a very noisy environment, such as a club or during soundcheck when the drummer is whacking the hell out of his snare drum.
2. A well-cut nut--this means a nut that is just perfect for the string gauge that you use. if it's too tight, when you use the tuner, the string will get pinched in the nut, and then when you bend or play, this pinching will give, causing the string to go flat.
3. Stable tuners--this is not as big of a deal, since most tuners--even the really bad ones don't slip.
4. Proper tuning technique--this sounds really STUPID, but it's EXTREMELY important. when you tune, always tune in the SHARP direction. let me give an example:
   
   suppose you are trying to tune the fifth string to A. currently the string is flat. In order to tune properly you need to turn the tuning gear until you hit A. If you go SHARP, the WRONG thing to do is to turn the gear down until you hit A. The reason this is incorrect is because there is still a minute amount of slack in the tuner--no matter how good the tuner is, there is ALWAYS some slack.

   for those of you who would doubt this, try overshooting your target note and then tuning DOWN toward the note. once you hit the note, take your finger and give the string a big yank. now check your tuning again--i GUARANTEE it's going to be flat, if only a few cents or so.

   If you go too far sharp, the PROPER way to tune is to turn the gear so that the resulting note is DELIBERATELY flat. In other words, going back to our example, if you overshoot your A note, then turn the tuner so you are FLATTER than A. now give the string a tug as you would do when you are stretching. the slack in the tuner will give. now tune towards the A, being careful not to overshoot. if you overshoot, repeat the process. The key is to tune in the SHARP direction only!

If you fail to observe any of these points above, you're going to be in a mess, because stable tuning requires all of the above elements to be in place. Likely you're going to find that your tuning problem is the result of a combination of the above factors--after following all of the above guidelines, I usually find that even the worst and cheapest guitars stay in tune just fine.