There are essentially two types of finishes that are used on guitars these days: Nitrocellulose and Polyurethane. There are others, such as waterborne finishes, but I'm not going to cover them here since they aren't very common on mainstream instruments. Nitro is a relic from the old days--but a couple of larger manufacturers such as Gibson and Fender still use them on some of their vintage reissue guitars. Nitro is very picky and doesn't age well. Poly is poly :D--if you've ever finished your deck then you've probably used it and seen how durable it can be. Polyurethane is very durable and you can clean it with slightly more abrasive chemicals--although I don't recommend it.
If you want the most out of your finish--whether polyurethane or the finicky nitrocellulose--then you should definitely pay attention to what's in your guitar polish. I personally don't use polish frequently at all. Instead I use some alcohol and a little distilled water on a damp cloth to clean the sweat and grime off my instrument. Then, whenever I do a complete ground-up restring I will wipe the body and fretboard down really well, then shine the body up a little with some polish and finish with a healthy dosage of mineral oil on the fretboard.
Your fretboard, depending on what woods it is constructed out of, should be paid special attention to. Rosewood, for example, is a very resilient wood but it can greatly benefit from an occasional rubdown with some mineral oil. I use Gerlitz Guitar Honey with much success. Mineral oil will bring out some beautiful colors in Brazilian Rosewood and other unfinished fretboard woods. A finished fretboard can be treated exactly like the guitar's body. To clean a fretboard, you can use naptha, or common lighter fluid, to cut through the gunk and grease or one of the many other techniques described by answers to this question.
In summary, be careful what you put on the body of your guitar. Stay away from very abrasive petroleum based chemicals, and certainly anything too basic or acidic. You shouldn't need a chemistry degree to understand what a polish will do to your instrument, but you will need to understand the general ideas I have tried to outline here.
