Unless you're support or troll.
Even if you're support, last hitting is important when your carry isn't in lane so that gold doesn't go to waste. But more so supporting your carry's last hitting - that is, helping them hit each caster minion once under tower before the tower hit so they can last hit easy, making sure to spread hits or attack only the seige creep when pushing so as to not mess up their last hits, etc.
And you can be super troll as supports like Soraka when your heal is level 1 and heal your minion right before the enemy goes to last hit. It survives and one of the enemy minions finishes it off instead. Cute little way to deny during the first level or two (they'd dive you to punish you for wasting your heal once they have more skills).