It is critical that cyclists and all athletes in general know their limits. By this I mean that you must know when you are helping yourself and know when you are damaging your body. This is true in micro and macro cycles.
Let's say that you are in a race that is quite long and you go beyond your limit for too long early in the race. In this case you will never fully recover and you will have a rough go for the rest of the race. Many of us will blow up completely before we back it down a notch. This is OK to do in training, but if you blow up in a race, your race is pretty much finished.
Now say you know that the pace on a big climb is too much for you to handle and you know that if you just go your own speed you will lose less time than if you blow up. In this case you have learned your body and are a smart athlete. Alex Zulle was great at this. There were many times when Alex came back on riders that unsuccessfully tried to stay with Lance and ended up putting time into them because they blew up from Lance's pace. If they had known their bodies and the climb, they would have been able to ride steady and keep the time gap reasonable.
It is important to know where that level is for you. One way to find your limit is to do lab testing to find your power and HR ranges. Another way is to pay close attention to your body when you get in those situations and figure out what you can and can't maintain in terms of HR and power. There is a caveat to always staying within your limits however. If you can manage to go over your limit for a short period and thus stay with the leaders to the top of a climb or until they exit a crosswind section, then you should do it. This will allow you to maintain the draft on the descent or in the head or tail wind section. In the long run, this will save you the energy of trying to chase back up. This is a difficult area to master and one that comes with experience. There are not many big climbs around here so I always go as hard as I can to stay in the lead group. However, time trials, like long climbs, are a great example of when it is important to know your limits. If you go too hard in the first 10 minutes of a TT' trust me when I tell you that you will struggle the for rest of your ride.
In short, learn your limits, sometimes you need to push past them to stay with the group, other times you need to respect them for the best result. The most important thing is to know where they are.