Here are the nonstandard methods I've used or seen used:
1. Roll twice. Take the better roll. (Raises the mean but keeps the same theoretical minimum and maximum).
2. Roll twice. If either roll is above the mean, take the better roll. If both rolls are below the mean, add them up. (Raises the mean more and almost abolishes below-average results; raises the minimum from 1 to 2.)
3. Reroll all hit points at each level. If the total is less than or equal to your previous hit point total, add one to your previous total instead. That's not one + con, it's just one, period. (Uniquely out of these methods, should keep the mean about the same; at second level and possibly for a little while afterwards, it actually *LOWERS* it. I suspect it actually raises the mean a tiny bit at high levels, as a really good roll is more likely to have a lasting impact than a really bad one, but overall it should keep you pretty close to the mean. Same theoretical minimum and maximum, but makes it even less likely that you'll actually be anywhere near either.)
4. Roll once. If your roll is below half the maximum (or to put it another way, less than mean - .5) treat it as though you had rolled half the maximum. (Obviously raises the mean and minimum, probably about the same mean overall as method 2 but I haven't checked in detail.)
5. As 4 above, except that you still get half the maximum even if Con penalties would reduce you to less than that. (Con *bonuses*, however, are treated as in 4.) Moreover, at first level, you ignore Con penalties entirely. (The same as 4 for most characters, but it makes a low Con somewhat playable.)
The last game I was a player in used 3, and I briefly did as well; both games I currently DM use 5.
EDIT - forgot these:
6. 1d4 + (normal maximum - 4). So for example, D6 would become D4+2, while D10 would become D4+6. This was originally from a document available on the net called Enhanced Dungeons & Dragons, which also allowed you to trade points from the fixed number part (but not the D4) for other benefits. (What I don't like about this one is that it doesn't help the characters at the low end, who need it most, very much if at all; on the other hand, for characters at the high end this is even more generous than 2, 4 and 5. As someone mentioned earlier high variance is harder to deal with than raising the mean, and this *increases* variance.)
7. 1d4 + (normal maximum -2). Uniquely out of all these methods, this not only raises the minimum and the mean, but breaks the taboo on raising the maximum. In fact, your mean result with this method is greater than the maximum result using the book rule. Obviously extremely generous; and the flat two extra points for everyone somewhat reduces the variance problem too (technically there's just as much, but it's easier for a 45 hp character and a 105 hp character to adventure together than if you replace those numbers with 25 and 85).