My high E string just broke, so I figure it's time for new strings. I'm using Ernie Ball Super Slinkies right now, but my guitar doesn't seem to stay in tune very well. I have an Epiphone SG, by the way.

Just wondering if there are any strings out there that will prevent slipping out of tune.
It's not the strings, it's your tuners. Or possibly your nut, like ghold125 said, but my money's on the tuners; if it's really bugging you you can get a set of Sperzels or something installed for not too much.
i find D'Addarios are teh best, but it's all personal opinion, every string is different
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i never notice a difference with tunig whenever i get a hair up my arse and change string manufacturers. its gotta be the equipment
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depends how long you've had the strings on...... old strings will go out of tune like that..... also, super slinkies are for people who like to change their tunning alot and so are very flexible(so much so that they are unrecomended for floating bridge guitars)..... but if your strings are new then it could be the nut or tuners...... get gotoh stuff if you're getting new parts
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Heavier gauge strings supposedly hold their tune better. I use .011-.050 pure nickel on a strat with the trem set to float, also I have Ferraglide saddles and I don't get tuning problems until my strings are like 6 months old.
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Ok, thanks for the replies guys. I'm gonna try out those heavier gauge nickel strings, like Schneiderman said, and I'll try out that stringing method that hell_monkey suggested. If those don't work, I'll get some new tuning machines/a new nut installed.