Reading about training for climbing, you can get the impression that the key ingredient is effort, expending energy and building power. While I would agree that such training is a vital part of becoming better at bouldering, for many a steady diet of such climbing becomes counterproductive leading to plateaus and stagnation. My remedy for this situation is to spend a few sessions doing lots and lots of easy yet creative climbing.
At Flagstaff Mountain, behind Boulder, where I spend a lot of time bouldering, there is a great concentration of boulders and formations offering a seemingly infinite number of problems at very easy grades. Within a few hundred square yards, I can find 30 or 50 short problems that allow movement of virtually any type on all kinds of holds and features, ranging in difficulty from 5.6 to V5. So occasionally I will spend 30, 45 minutes or more climbing continuously on this kind of terrain, never stopping to figure out moves or try the problem twice. I also try to work in downclimbing and traversing to connect problems, always trying to maintain the flow of movement.
Why does this help make you a better climber? It works in a number of ways. First, you are spending time climbing instead of sitting around, moving gear, chatting with friends, taking off shoes, etc. So you are upping the volume of climbing considerably and aiding in general aerobic conditioning. In one of these typical sessions I am probably logging between 400 and 600 feet of climbing in under an hour. Second, by emphasizing continuity of movement, you are building better balance and smoother transitions between moves and stances, the kind of movement skills that can help considerably in much harder contexts. Third, you are experiencing multiple climbing situations in rapid succession and problem-solving quickly as you move through them, a learning exercise that allows much faster ascents and even flashes of harder problems. Fourth, you are building in greater variety of grip and body positions, helping prevent injury and strengthening little used muscles. Fifth, by building the sense of flow in a comfortable and low-stress way, you are aiding the formation of robust subconscious muscle memory that will assist you when you are tired and under stress, as in a problem at your limit. Shaping practical and productive movement patterns that you can maintain even in marginal situations is what climbing training is ultimately about.
Circuits can't replace the hard work of developing the pure strength required in developing finger and arm power. But they can help train that power to work more productively and can allow a good training day when the "snap" just isn't there. You can also use this kind of training as a great warmup, provided you keep the difficulty very low and don't get pumped. One key is continuous uninterrupted movement, which when you think about it is very rare in most bouldering sessions. The other is avoiding repetition of problems you have wired in the same order and the same beta. Seek new problems, contrive different sequences, and constantly see possibilities for new easy problems in order to keep the session fresh. Varying pure power sessions with a few of these easy circuit days may be just the remedy for that heavy burned-out feeling from too much training.