My group plays with some of the Pegasus expansion (no Caprica board, but the Pegasus ship board) and the Exodus characters, extra loyalty cards, and skill cards but nothing else from Exodus (no cylon fleet, ionian nebula, or conflicted loyalty cards). We generally enjoy this mix, except...

One thing that our members are repeatedly finding is that most of the fun of the game is the paranoia induced by not knowing who the cylons are. However, our only real fear is what the cylon might do if they get a "great reveal," that is, being able to screw the humans with a combo of a failed skill check right before their turn, using their OPG in a bad outcome, or getting an XO where they do something awful, and then use their reveal power as a kicker. Short of this, however, the unrevealed cylon's power to sabotage the humans in most other ways have been fairly pathetic. The ability of the humans to catch cylons being secretly sabotaging is very high - and unless the cylon has the next turn and can escape, they often get brigged or airlocked or Cally shoots them, etc. While there have been some great games where unrevealed cylons kept the humans paranoid, fighting one another, wasting time, it's never been clear if any of this outweighed what they might have been doing as revealed cylons - which, with the Pegasus expansion cylon locations, is generally spending 2-5 turns doing nothing but collecting super crisis cards and then going crazy with them. The latter is not fun for anyone, but it seems more damaging than staying hidden and often having to keep helping the humans in order to stay maximally hidden (nothing I hate more than as an unrevealed cylon realizing that the positive skill card I felt I should play to stay hidden helped us overcome a crisis). In the core game, an unrevealed cylon who got found out and brigged could even be more effective by being able to openly sabotage as many crises (with one card) and space battles (with die roll modifications) as possible, but with the Pegasus Airlock, the human players are not going to hold back from simply killing off the stubborn unrevealed cylon who refuses to come clean when it's obvious what they are.

So, in general, what should stop a cylon who, from the start of the game knows they are a cylon, from revealing themselves almost immediately, and on their own terms? Why not just go get as many super crisis cards as possible (or whatever it is you think works best)?

I mean, other than it makes the game much less fun?

I've played dozens of games (probably over 100 at this point) with the base set, with Pegasus, and a few with Exodus now, and I think the answer to this question is largely dependent on how many players you usually have in a game and where the Cylons are sitting at the table. With more players, turns get fewer and the action you take on your turn becomes more and more important; with less players you will get a lot more actions over the course of the game, so you can probably afford to waste a few. Collecting SC cards can be an effective way to try and end the humans, but it only usually works if the Cylons hit them so hard at a crucial time that they can't ever recover. Considering that each SC you draw beyond the first one (with a reveal) costs 2 turns (1 to draw it, 1 to play it) and in the meantime the Cylon player isn't really able to mess up skill checks or spread suspicion, it may actually end up being the least effective way for the Cylons to win. You can't really predict what SC you'll get, and you may use a lot of actions to get cards that don't help much... for example, the "activate all ships" SC doesnt do much good if there aren't ships on the board when your turn comes around, and an attack SC might not be useful if Cain is sitting to your left and can just jump the fleet away after you play it; Bomb on Colonial One is pretty useless if the President isn't sitting there drawing Quorum cards. A Cylon who reveals early can sit and collect plenty of SC cards, meanwhile, the humans are easily passing skill checks, ensuring resources are managed properly, and making plenty of progress on the jump track while they scout for good destinations.
Generally speaking, imo, keeping the "humans paranoid, fighting one another, wasting time" etc will probably hurt more in the long run than just playing a SC several turns in a row later in the game. You also have to keep in mind that the longer a Cylon stays hidden, the more opportunities they have for that "great reveal" you mentioned - a very early reveal won't hurt nearly as much as a well-timed reveal later. For example, revealing and sending someone to the brig or damaging Galactica twice early in the game is pretty easy for the humans to recover from - repair the locations, get someone out of the brig and move on, whereas a later reveal with one of those cards could send a pilot to the brig in the middle of a fierce battle or damage the Armory after Centurions are on board and will put a lot of pressure on the humans for a bit and may result in bigger losses overall. Another important things to consider is your OPG, staying hidden as Starbuck or Helo or Boomer can make a big difference if you can OPG the right Crisis card and it can hurt more than revealing in some instances (Starbuck bouncing the Legendary Discovery Crisis makes the humans cry). You are correct in stating that the humans should be able to catch Cylon sabotage pretty easily; spiking skill checks is a bad way to try to hurt the humans, there are much more effective strategies (hold the big value cards so no one else can get them, overplay into skill checks, let them brig the wrong person, etc). Also consider what titles you have or may soon have - spiking a skill check that sends the Admiral to the brig upon failure and also bumps you into the Admiral slot is probably worth it; a Cylon President that manages to get his/her hands on 2 Arrest Orders is worth a few turns of helping the humans early so you can toss 2 people in the brig off of an XO and then cackle gleefully as you run around an empty ship moving civies into fleets of Raiders and such.
Frankly, the most effective Cylon players in our games will help the humans for the first half of the game, not give anything away, and wait til the Sleeper Phase before revealing. A combination of one revealed Cylon and one still in hiding is often the most deadly, especially if the revealed Cylon can figure out who his/her partner is and the humans are still in the dark; even if the revealed player doesn't know who the other Cylon is, it can prevent the humans from abusing XOs since they can freely play one every turn once the Cylons are all revealed. It also allows the unrevealed Cylon a lot more leeway to hurt skill checks since it gets a lot harder to count cards once a revealed player is making a mess of each one. The main problem with a very early reveal and collecting SC cards (or whatever strategy you go for) is that it severely limits your options as a Cylon and can pigeonhole you into a strategy that might not work.
Exodus does change all this a bit if you are using more pieces of it, and I'm starting to wonder if at least one Cylon should reveal ASAP and go to town on the Basestar Bridge... and wow this got lengthy...

Thanks for your detailed, thoughtful reply, Skowza. You make a lot of good points about each game being different based on the position of the cylons around the table and the number of players, not to mention the characters you're playing. I also agree that an early reveal (damage, a character in the brig) can be more easily overcome than a reveal at the right moment that overwhelms. I also agree that a total super crisis card approach can limit you to the fate of which SC cards you get - there's nothing like getting the "Human Prisoner" SC card to make for a depressed cylon.

I will just say that I've tried several times to "wait it out" as a cylon and look for the right moment to reveal or try to find good ways to hurt humans, but there have been a number of ways for the humans to reveal me without my doing anything wrong - crisis cards that allow a loyalty check, quorum cards, and Baltar's OPG. Sometimes you just get called on.

The base game, I think, offers cylons a less risky path for staying unrevealed, compared to Pegasus, because they can't be executed. The base game also offers just one super crisis card but also a much more powerful Caprica location and Human Fleet locations. So, I think part of it is that we play a lot of Pegasus and it pushes us a lot more toward the Super Crisis approach.

When we play Exodus more fully, I will be wondering how much of the Pegasus expansion to keep playing alongside it. There are so many elements one could debate bringing over or leaving behind - the characters, the crisis cards, the treachery cards,the Pegasus itself, the "updated" Cylon locations. I would like to influence the game in such a way that it allows for some renewal to the game through more flexibility or surprises.

@Anacreon

Note that all of these loyalty revealing options only make your loyalty known to one player, who is under no obligation at all to tell the truth about it. If you can make the other characters doubt that person's statement, you'll get a few rounds respite. Balthar in particular is the least of your concerns - he say's you're a cylon. So what? Statistically, he's twice as likely to be a Cylon as you, pre-sleeper phase. Draw attention to his second loyalty card and every questionable action he ever did. If he's not the president, demand that he be tested by the president - which will at least waste a valuable cylon mugshot.

@ Cifer: Yeah, I do know - and we've had many "He's lying! He's the cylon!" and "No, I'm not! She's really the cylon!" exchanges. You play with the same group enough times, though, and it's hard to keep a straight face...