Currently its the d4, as my current character is running around with daggers, lt. pick, lt hammer, and is a ranger and those are light weapons. But in the past its been d6s d8s and d10. Alas the lonely d12 barely gets rolled.
I think for non-GMs, it's all about what class you play. Rogues, wizards and sorcerors are going to use D6 more; bards, clerics and druids are going to use D8 more.
Omitting D20s, the dice rolled most frequently will be the damage you inflict. Almost all damage-causing arcane spells deal damage with D6s, whereas divine spells use a wider variety of damage dice. When it comes to weapon damage, rogues naturally tilt towards D6 thanks to sneak attack damage; in addition, most weapons oriented towards rogues and wizards tend to do D6 damage whereas bards, clerics, druids and sorcerors are more likely to end up with weapons that do D8.
When it comes to barbarians, fighters, rangers and paladins, too much hinges on weapon and shield choice to generalize about the class. Obviously, shielded characters (and rangers who take the melee progression) of these classes are much more likely to use D6s or D8s than those who do not use shields.