Our opponents putting in raises pre-flop is for the most part a good thing. Whenever opponents play straightforwardly, it gives us valuable information as to their possible holdings. They are telling us they have a very good hand, and of course it's better to know this up front, then find out later after we've lost money to it we didn't have to.
The first task in dealing with these raises is to gauge the frequency of them. The first part of this is determining how often opponents put in PF raises generally. This will tell tell us things like how tight we're going to have to play in earlier positions. If there's a lot of PF raising, then we're going to have to throw away more close hands early, and if there's less, we can play a few more. This is of course because we don't want to have to call raises with these hands, and if it's likely we do, we won't play them as much, but if it's likely we don't, we will play them a little more.
Also, generally speaking, we can put in a guess as to the quality of the hand being raised with not only by seeking out the cards at showdown, but simply by the frequency of the raises as well. If there's a raise pretty much every hand, we know that the cards being raised with aren't the super premium ones, since they don't come up that often. Or if a raise is much more rare overall, we need to be more careful, since it's probably a very good hand. This is even more important when it comes down to gauging the frequency of raising among particular opponents, to decide what sort of hands he is probably playing in these situations.
As well, we need to watch what position the raise is coming from. This is more of an issue in better games, but we can look for patterns in particular opponents' play in certain positions. For instance, usually raising on the button indicates a positional raise rather than one based purely on the strength of one's hand. Or a raise late and first in, which may be more of an attempt to steal the pot.
All this is going to give us valuable information as to what we should do when a certain opponent puts in a pre-flop raise. We want to be careful of these hands though, as the potential to lose money is greater typically, since the hands we're going to be going up against are generally going to be of a better quality than normal.
What we don't want to do here is waste bets by calling, only to be faced with a raise downstream, where you have to get out of the hand. At limit, if you figure that good players will make 2 or 3 big bets an hour, money you throw away here can be the difference between winning and losing. Every bet you save is a bet you've made. There's of course going to be times where this is unavoidable, but you want to keep this to a minimum by paying attention to both position and the tendencies of your opponents downstream when selecting starting hands.
Even worse than this though is the habit many players get into of limping in then pretty much automatically calling a raise, or even several raises. Generally, if your hand isn't worth a raise, it certainly isn't worth calling one, since it takes a stronger hand to call a raise than it does to raise in the first place. This is because the likelihood of your having the best hand, the primary reason why you're raising, is reduced as other people raise and indicate more strength.
What happens in this case though is that if you've got a decent or better hand, but it wasn't worth raising with, your cards may easily be dominated. For instance, you have KJ. If you call a raise with this, and miss, you've lost an extra bet. If you hit it though, you can easily lose a lot more. Opponents don't generally raise with weaker hands than this, but if they have AA, KK, QQ, JJ, AJ, or KQ, you're probably in big trouble. There aren't many raisable hands that they could have in fact which would place you at the advantage.
So what ends up happening is that you lose more money on this than you would have if you folded to the raise, and so it's a good idea not to get involved with these hands. An exception would be if your cards are live, for instance, with a pocket pair, and there's a fair number of people in the pot. In this case, at least if you hit your hand you will probably win the pot, as opposed to when you are probably dominated.
On the whole though, it us usually advisable not to want to participate in raised pots unless you have a stronger hand than you would normally require. This is common sense really, but it's surprising how many players, particularly the weaker ones, don't take heed to this. Their eyes light up at the prospect of more money to be won, not appreciating that since they are probably at a disadvantage, over time it is their opponents who will be winning these bigger pots, with a good chunk of their money thrown in.
As we want to become involved in hands that we are the favorite, a good rule of thumb is to calculate what the average type of hand that is raised with is, and make sure yours is better. And not throw good money after bad when it makes more sense to get out than stay. This way you'll make sure that you don't make the mistake a lot of players do, and get burned when you should have known better.