i daily drive around 3kw continuous power.. on a stock 60 amp alternator.... no capacitors... and this is toned down... i use the same vehicle to compete with and for competition i use about 12,000 watts continuous... no capacitors...
caps are harmful for competition use.. when they discharge during a test tone, which is long before you end the tone, they will start taking juice away from your amps in order to refill themselves.. however, for musical purposes, they are helpful, because a bass hit is a short burst.. afterwhich the electrical demand drops and the cap can refill..
your alt has more than likely gone out due to a faulty alt honestly.. unless you have been blasting with far more than your alt can put out with a single stock battery... for a long time i had more than enough stereo to shut my engine off with the twist of a knob.. i upgraded the charging wire on my tiny alt, upgraded the engine and battery grounds, and ran a better battery.. that worked for a while until i upgraded, now i run the same battery up front, an orbital blue top and an optima yellow top out back.. and no it doesnt matter if you run mismatched batts and no you dont have to have an isolator.. all industry nonsense they are pushing to sell more..you can run an isolator, it has its benefits, but not in every car....
Guys, caps are band-aids for a gashed up wound. If your lights are dimming, get a better alt. Check out all the research Richard Clark has done on this subject.
Andrew and Stephen also had good, informative, truthful posts.
As a little side note: if you don't know what you're talking about, don't post something like you know what you're talking about. Some people who aren't knowledgable of these subjects might believe what you post without double checking. This is one of the reasons that the car audio world is full of stupid myths!