In D&D3e, if you successfully hit a target you always did at least 1 point of damage (before applying Damage Resistance), even if you had a Strength penalty. I can't find any mention of that rule in the 5e PHB. Does the rule no longer apply, or did I just overlook it?
It is correct to say the 3.5e rule no longer appears in 5e. Another tweet (god I wish we had that back in the 90s) clarifies that the minimum is indeed 0.
There is not a damage minimum of 1, so it is possible to deal 0 damage with an attack.
@JeremyECrawford Do attacks do a minimum 1 point of damage, or would an unarmed strike from a goblin (STR -1) do 0 damage?
There is no such rule in 5e.
An unarmed strike by someone (other than a monk or tavern brawler) with less than 10 strength will never do any damage, (even on a crit), for example.
There is no damage minimum rule, on the contrary sources of damage can deal 0 damage.
SAC V 2.6 P 13. says:
Can damage be reduced to 0 by resistance or another form of damage reduction? There is no damage minimum in the rules, so it is possible to deal 0 damage with an attack, a spell, or another effect.
According to the Basic Rules, it is possible to deal 0 damage (but never less):
With a penalty, it is possible to deal 0 damage, but never negative damage.