Shields Shall Be Splintered
This is one of my favorite house rules. No particular need to restate it here (here's the original, from Trollsmyth), but I'd use an expansive interpretation, as in this. Also, here's a great post from Jeff Rients about this kind of thing.
Characters wielding a two-handed weapon would roll their damage dice twice and take the higher number.
Characters wielding a weapon in each hand may make one attack per weapon (on the same target), but when rolling damage, roll damage dice twice and take the lower number.
Exploding Damage Dice
From this Daily OSR post: "All damage dice 'explode' if they roll the highest possible number on the die. When exploding, count the score, then roll the die again and add that. Keep going until no dice score the maximum. This applies to all sources of damage.
For example, if a character falls off a tower and takes 3D6 damage, the dice might come up 3,5 and 6. Roll the 6 again and score a 4. Total damage: 18 points."
From this D&D with Porn Stars post: "Here's the deal: if you want to do something real specific--like hit the orc's torch and knock it on the floor, you can if you roll a crit. You can also extend your crit range as much as your heart desires: natural 19-20, 18-20, 16-20, all the way up to 11-20. Your choice.
The only catch is you then have to extend your fumble range from one by the same amount."
I understand that class-based weapon restrictions have a long and storied tradition in old school gaming, but they've always bugged me. I was thinking earlier about starting a new campaign and using the Swords & Wizardry White Box rules, and the cleric's restriction to bludgeoning weapons (because of a religious obligation not to shed blood!) really jumped out at me.
I wrote before about using class-based damage in the game high school game, which I thought worked quite well. If the main point of having class-based weapon restrictions is to safeguard the fighter's ability to do damage, class-based damage does the same thing just fine, without the side effect of needing to police other classes' weapons. It also fits in nicely with my preference for keeping "shopping" in character generation to a minimum. I don't particularly like the experience of players all closely reading over the weapons lists to find the ones which are highest powered, and using class-based damage would encourage players to choose weapons based on what they think would best fit their character idea.
I think that about sums up where I'm at for now. Still thinking about individual initiative versus side-based. I've always used PCs all go at once/Monsters all go at once in the past, but we've been using individual initiative in the campaign I'm playing in now, and it's actually been really fun. Maybe more fiddly than I'm looking for though, we'll see.