In League of Legends, many single target abilities can be activated simply by clicking on the opponent, much like an auto attack. These are all but impossible to dodge, short of using a Zhonya's hourglass, or being lucky enough to play one of a small subset of chamipons (Hello there, Fizz.) This kind of harass I find extremely annoying, simply because the only way to effectively avoid it is by staying away, which typically results in losing minion kills and therefore the lane. (Quick note: I'm referring mainly to those abilities which are ranged. Things like melee auto attacks don't bother me, simply because they have to get to melee range in the first place.)
To give a concrete example, the other day I was laning against Zilean as Orianna. Any time I was anywhere near him (be it to last hit minions or whatever), Zilean would place his time bomb on me, which after a couple of seconds explodes for major damage. While Orianna has a shield, it's not enough to block the damage from the time bomb, and to add insult to injury, Zilean can hit me with another time bomb while the shield is still on cooldown.
Orianna simply doesn't do enough early game damage to out-trade the time bomb, and even trying to do so would result in severe mana issues (considering I'd be using Command: Attack-Dissonance and Protect to reduce my damage, compared to him using one ability.) In short, the only way to avoid the damage is by staying out of range, giving my opponent a large advantage in farming. If there's some better way to deal with this, I'm very interested in learning how.