There are many fine poker books available to help you understand what kind of starting hands are playable and what aren't, so let's leave that problem to the books, and focus on all the good things that can happen when you fold and STAY FOCUSED ON THE GAME while you are not involved in a hand.
Learn More About Particular Opponents
"Good thing" #1: You'll learn more about how your opponents play. This is especially valuable if you know you'll be seeing them again, but valuable even if you're pretty sure this is a one-shot appearance. Discovering who is a rock (tight player) who will bet only the nuts (the best possible hand) is very easy and very important, but I'm amazed at how many players don't track this, and pay these types off when they've shown nothing but the nuts for hours or days on end.
There's a lot more you will learn than who is a rock, though. You will learn who likes to play only in late position. Once you find that out, you'll be much less afraid of their raises (although they'll still have position on you when they make them!). You'll learn who likes to see a lot of flops but who gets out when they miss a flop, who will lay down hands on the end ... the list is almost endless.
One problem with collecting this kind of information is that a lot of times you start to collect it and then can't finish, because the player mucks his hand and so you can't really be sure what cards were there. Another problem occurs when you try to study too many players at once: by trying to learn everything about everyone simultaneously, a lot of times you learn nothing about anybody.
Consider Studying Two Players At Once
I prefer to study two players at a time, usually at different sides of the table. That way, it isn't obvious that I'm always staring at the same person, since I'm looking in different directions. Because most players are actors (usually grade B or C actors, but actors nonetheless) it's fairly important to do your studying as discreetly as possible.
Don't disdain studying players you consider to be worse than you. You may learn how to take even better advantage of their weaknesses, but you might be surprised to find that you can learn a lot from weaker players. There are so many moves in poker (I love the old John Bonetti line, "I got so many moves, sometimes I don't know what I'm doin" myself"), and so many different skills and ways to be good, that even someone whom you correctly judge to be inferior to you overall probably does one or two things better than you.
If you try to follow a person's play all the way through to the end, you might learn something you might want to try yourself later, or failing that, might learn something about the way a particular kind of player (although be very careful about pigeonholing players into groups) plays a certain kind of hand.
If You Won't Fold, You're Probably Doomed.
I guess what I'm saying is, the best cure for the boredom that leads players to play too many hands is recognizing how incredibly important it is to study other players. If, knowing that importance, you still find yourself unable to fold and watch, you're probably doomed to one of several fates:
a) You won't improve, but your opponents might, so your results will worsen (the most likely result).
b) You might have to move up to higher limits, against tougher opponents, before you have the incentive to put in the hard work.
c) You might improve, but only in the aspects of the game involving your own cards and play, which will put a very severe cap on how fast or much you improve, and on what kinds of games you'll ever be able to join successfully.
So when you pick up a mediocre starting hand, throw those cards away, and instead of watching the game on TV, watch the game going on right around you! It will likely provide the most valuable free lessons you'll ever get.
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Vary your playing strategy. The player whose game is always the same becomes an easy mark for smart poker players.
