Weapon damage.
Spell damage.
Attack rolls.
Skill/ability checks.
I leave 'saving throws' off because I'd much prefer to see those as target numbers against which active characters would make rolls. To be fair, though, this would leave the results just as random.
Now, I would very much like to see a lot LESS randomness in all four of the above types, but I recognize my reasons for that as being somewhat personal and not widely applicable.
In general, if something is PERSISTENT (hp, ability scores), I don't want it to be random. If it is INSTANTANEOUS or has a short DURATION (attacks, spells, skills, ability checks), randomization is fine, because it will tend to average out over the course of a campaign.