Do you prefer to use real dice, a dice application or program, or use a diceless system?
Definitely physical dice. I love the feel of dice in my hand (especially when I’m not doing anything) and the sound of them clattering into whichever miniature I’m having a problem with today. I especially like having dice of different colors. It lets me roll several at once for different targets, differentiate them by effect (grey dice are the greatsword, red is the fire, etc.), and match them to my character. Here’s my dice case today:
Row 1: My first die and the giant d20 I use for countdowns, round indicators, and other things I want players to see easily; a slew of orange d20s from D&D poly sets and the miniatures game, along with d20s in several colors so I grab them without shuffling around in row 2; Fudge dice, dice with colors instead of numbers, and dice where the faces have pictures of my players on them; tokens from early 4E boxes in case I’m in a situation where I don’t have minis.
Row 2: A poly set in each of several colors, translucent when I can get them and pretty when I can’t. The first nine sets also have a second d6.
Row 3: Collections of d12, d10s, d8s, d6s, and d4s, in that order. These are mostly the rest of the D&D poly sets, plus split up poly sets I don’t use often enough to get a spot in row 2, plus a set of twelve d6s for when I need to roll a ton of them as for falling damage.
Row 4: A light-up d20 I got as a gift, three more pink d20s for when I played a character who attacked four times per action, and another d20 whose origin I’ve forgotten; markers, in case I’m not near my good ones; assorted Warhammer-style d6s including my oft-used scatter die.
This is the full set I usually use when I’m DMing. If I’m playing in a campaign I have a small bag to carry only the dice I need. I’m happy enough with my current setup that I haven’t gotten any new dice in a few years, so I expect to stay at this level for the foreseeable future.