I played two such characters, one in DnD-3.5e, and the other in DnD-4e.
The first was a human Swordsage, that used maneuvers and stances from the Desert Wind and the Shadow Hand schools. When he was in his "manic" state, he used only Desert Wind maneuvers, and he was flamboyant, happy, social and even foolhardy. When he was in his "depressive" state, he used Shadow Hand maneuvers, and was sneaky, reserved, taciturn and very cautious. The switch in personality came depending on the situation, but some strong emotion (anger, fear, lust) made him change personality instantaneously. My DM didn't like the character because it was a little unpredictable, but it was very fun to play.
The second was a genasi Swordmage, that had the Firesoul and Airsoul manifestations. The personalities were similar to the first character, and he used only elemental powers with the fire or ice keywords depending on the current manifestation. The switching was also similar, but he could switch personalities (and powers) during combat for the duration of the combat. When he reached paragon tier, he could go Stormsoul when using an action point...and that was his "real" personality, but emerged rarely. I planned to develop it further and by epic he'd be more Stormsoul that the other manifestations, but our campaign stopped. I was both DM and player, and while it was difficult to play a double character and be a DM, it was very funny and entertaining nonetheless.
The point is that if you can make the character fit in the game world, and if you don't abuse the mechanics, you can even bend the rules and have a great game experience. The alignment is not a problem in 4e, but in 3.0e and 3.5e could be, and it makes for even greater fun to switch whole classes (not only powers). If your DM agrees to bend the rules slightly, you will have a lot more fun, with a little more roleplaying effort.