Twilight Sparkle: Depending on how much alcohol she imbibed, I could imagine her as either extremely gregarious or just very mellow. I suppose it would depend on both the amount and the context of the drinking. I suspect she would be something of a social drunk, elaborating on her studies and other esoteric subjects. If Twilight read up on drinking, she might know to pace herself. It can be difficult to gauge the extent of her naiveté.
Pinkie Pie: For laughs and giggles, Pinkie would become "normal" when drunk. My preference for Pinkie is not so geared toward the arguably predictable. Given her preference for sweets, Pinkie might prefer alcohol mixed with fruity, sugary drinks. Therefore, Pinkie would probably become exceedingly excitable, dumping the few inhibitions she normally retains.
Fluttershy: The comedic contrast for drunk Fluttershy would be for her to become loud and expressive. In my opinion, however, she would probably either refrain from drinking or would be a drousy drunk.
Applejack: I suspect that she has had exposure to liquor and alcohol, if the Apple Family apple cider is any indication. AJ is a physically tough country gal, permitting her to down more alcohol than the usual mare. When drunk, AJ might be chatty and painfully honest in all of her observations; as Silly Lily mentioned, I could also imagine AJ engaging in drunken competition quite readily.
Rainbow Dash: I woud be she is a speed drinker, quickly tanking up before inebriation hits her like a tidal wave. Dash might violently oscillate between being a gregarious, playful drunk and being self-destructive and hyper sensitive. In other words, when combined with a sloshed AJ, it could be a powder keg waiting to explode.
Rarity: A lady would never let herself be overcome by alcohol. Rarity would therefore rarely if ever get herself totally smashed. When intoxicated, Rarity might remain very sociable, albeit she would probably be a chatbox.