Since standard D&D is balanced assuming both the PCs and the monsters have average hit points, we play "as the die lies" for HD rolls, with two exceptions: max hit points at first level, and everyone gets one free reroll once in their character's career at any time they level and roll poorly for their HD. You have to keep the second roll, though, even if it's worse.
As for the coolest house-rule, I'm not sure; we keep pretty closely to the core rules as much as is possible. If I had to guess, it would be that in our games level-draining spells and effects don't actually result in permanent level loss upon a failed save. Instead, you just go in the hole XP-wise as though you had lost a level. The D&D mechanic of losing a level has never been clearly defined: do they actually expect us to track when and where we put each and every skill point, or remember exactly how many hit points we rolled for each level? Our method still retards advancement, but without the headache of reverse-engineering your character.