Under a regency, the regent's stats are used instead of yours (that's why your councillors are usually assigned-- they have the best stats) for realm diplomacy, stewardship, martial, the whole deal. Therefore, it directly affects your efficacy in all diplomatic interactions, directly affects your global tax modifier, directly affects your land morale, morale recovery rate, and sometimes how fast your realm falls to sieges, among other things. In addition, I don't believe they get the "1/2 the wife's stats" bonus, regardless of whether they're married.
In the case of being a child ruler under a regency, the amount of negatives is sky-high. [Succession wars, inability to command, opinion maluses of various sorts, personal diplomacy with all your vassals sucking terribly due to lack of stats/traits, regents trying to steal your throne (I've heard), the fact that anyone with a weak claim on any of your titles-- even a woman-- can have their claim pushed against you in some foreign court until you're an adult, etc.]
For other regency cases (pretty much only leaves incapacitation, unless you went on a pilgrimage, in which case most everything is shut-off and it's brief anyway), a lot of the intrigue decisions are disabled, and you can't join/lead factions or plot. Incapacitation does hurt the stats a bit too. Usually the game kills you off soon enough (realistically) in these scenarios, though I've seen an 'incapable' regency go on for over a decade; there should be a "abdicate" option in the decisions menu that allows you to abdicate to your heir and doesn't actually go to Game Over, despite having an heir of your dynasty. However, CKII doesn't handle voluntary abdication well, so the option would pragmatically have to be "Commit suicide," which seems a rather limited option.
If you want complete inability to do anything while in a regency, just open the console, and type observe until the regency is over. Then deal with the mess that the AI ruler made during the regency. That's the most elegant solution that I have for you.
EDIT: Oh, duh, I forgot about the imprisoned-regency case. Still, you will miss most events in prison, and miss all the stuff a child ruler misses, except for the succession and weak claims war threats. Yeah, though, this is another case where you might want to hit observe too if you want to role-play it. On the other hand, you can just not do anything (even though the game lets you-- which is also something we can't mod, FWIW) if you're in such a regency to role-play it and then enjoy a better view of the intrigue going-on first-person.
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