I have Limit Breaks in their own section, but I just want to mention a couple of extra things here. Namely, I'm talking about the best ways to increase you Limit Levels.
Getting your second Limit Break within a level is the easy part. The fastest way to do it use a Hyper to make your guys, well, hyper, and then give them a Cover Materia (don't worry if you don't have more than one, just get the Limit Breaks one person at a time). This ensures that they take more hits, and that their limit meter increases faster. Unfortunately, you can't speed the process even further by hitting your own guys, but you can Manipulate the enemy and make it hit you. This is probably the easiest and safest way to do it, since if one of your characters is running low on HP, you have all the time in the world to heal him/her. Anyway, once their limit meter is full, use the limit. Do this 8 times, and you'll get the next limit within that level.
Getting to a new Limit Level is a little harder, and takes some patience. You'll need to defeat (and this means deliver the killing blow) 80 enemies, for most characters. The absolute best place to go is the Mythril Mine, where enemies attack in fairly large packs and are easily beaten, even early in the game. From the very first time you go to the Mine, just give someone an Enemy Skills materia with Matra Magic, and fire away until he or she gains his or her next Limit Break! Matra Magic, which can be learned from the Custom Sweepers roaming around the Midgar Area, is the best spell to use, I think, because it only takes 8 MP to cast and takes out in one shot every monster in the Mythril Mine except for the Arch Dragons, which usually need to take one more hit from a normal weapon to kill. Using these strategies, you can actually get all your Limit Breaks before you even reach the Junon Area for the first time! Yes, it takes an hour or two extra, but if you're like me and like to get things out of the way as soon as possible, then it's well worth the time spent.