For pretty much all of the character generation things - ability scores, hit points, background traits, descriptive details, etc. I leave it up to the player if they want to get dice involved or stick with more reliable methods such as point buy. My own preference is generally to roll for ability scores and do most of the rest manually, but I know players often have strong preferences regarding character generation methods, so I let them choose. I don’t find there’s generally much of a balance issue between the various generation methods, so having different characters generated via different methods in the same party is perfectly fine with me. Though, I house rule that the folks who roll for hit points can re-roll 1s, to bring the average in line with taking the fixed value.
For DM-side stuff, I like using lots of dice. Random encounters/complications (including things like planar effects), treasure hoards; I even randomize the resale value of valuables like trade goods, gems, and works of art. I do prefer to design dungeons by hand rather than generate them randomly, but something random tables can be a good source of inspiration for dungeon design when I don’t already have an idea. I do roll monster damage, and like the idea of rolling for monster HP, but don’t often do it because then I’d either have to note each monster’s HP individually which would take up a lot of extra page space, or roll at the start of combat which would take up a lot of table time. Not usually worth the tradeoff for me. Would probably be easier on a VTT, but I’m a diehard pencil and paper gal.
One unconventional thing I like to do is "roll one and multiply." Like, when someone casts Fireball, I'll ask the player if they would like to roll the prescribed handful of dice, or if they would like to just roll a single die and multiply the result.
Rolling 10d6 vs. rolling 1d6x10. The player casting the spell chooses before the damage is rolled, and cannot change it or reroll it ever, for any reason, no matter what class feature or feat or divine intervention or anything else might say otherwise. The die is cast, literally.
Why would someone choose this? Well. Choosing the 10d6 option will almost always give you a reliable, middle-of-the-road result, with almost no chance at all of rolling maximum or minimum damage. There's nothing wrong with that. But choosing the 1d6x10 option gives you a pretty decent chance of getting maximum damage (16.7% chance, actually), and sometimes you really need to "go big or go home." Unfortunately, it carries an equal chance of rolling minimum.
It's certainly not everyone's cup of tea, and we don't use it every time, but my players like it. They're perched on the edge of their seat while the wizard shakes her fist over the table, blowing on her special "lucky d6," the tension around the table so thick you can cut it with a knife. And nothing beats the rush of seeing that nat-6 when you really, really, really need it...the room explodes with cheers and high-fives all around. Good times.
When you're playing D&D, dice can be used as often (or as seldom) as you wish. The way you use dice, or don't use them, can say a lot about the kind of playstyle you enjoy and the type of game you run. As a player, do you prefer to roll for your starting ability scores, or would you prefer to pick them a la carte? As a DM, do you randomly place treasures in your dungeons, or do you pick treasures from the appropriate list?
The poll assumes that you are already rolling for things like attack rolls, ability checks, and save throws...there's no need to check those boxes (if that assumption doesn't quite apply to you, scroll to the bottom of the list.) But what about all the other fiddly bits? Check all that apply, and add any nuance in a comment.
The poll assumes dice aren't killing characters because TRUTH that's what they do. We can run a one-shot right NOW and I'd sit back and watch that d20 peel the skin off your PC and you'd be asking me 'can I roll to avoid my roll?' UH. 'Roll to avoid your own roll'. Players think they are SO SPECIAL AND SMART until the dice ............... I KNOW what they do. In the game I'm designing in the GM advice I EXPRESSEDLY tell GMs to warn players about relying on dice rolls. It's self-mutilation disguised as fun people.