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.
Best Answer
First, what you call "point & click abilities" are usually refered to as "targeted abilities".
I see four ways to deal with this kind of harrassing champions. Depending on who you are exactly facing, some methods are better than others.
Out-range them. Targeted abilities typically have shorter range than true "skillshots" (non-targeted abilities), e.g. Ezreal's Mystic Shot or Nidalee's spears. If you choose this approach, stay within the range where you can hit your enemy, but he can't hit you. For example, Ryze is very weak against Cassiopeia for this specific reason.
Out-sustain them. Some champions have very efficient regenerative abilities, e.g. Warwick, Vladimir, or more recently Aatrox. These champions can't be killed simply by being harassed. Let them waste their mana on you while you keep recovering from your wounds. Zilean can't heal himself, so eventually he will have to go back to his base before you do.
Shield against their attacks. Champions like Shen are great against harassing abilities, especially if you can easily foresee when you will take damage, because your shield will absorb most of the damage taken. This is, is my opinion, Zilean's greatest weakness.
Attempt to crush them. This is the high risk-high reward method. Champions such as Talon (melee assassins with a gap-closing ability) are efficient against squishy targets, because their full combo deals a scary amount of damage. When the enemy moves towards you to harass, analyze the situation. If you think it favors you (= the enemy jungler is far enough, your opponent is not under his tower, there are enough allied minions and not too many enemy minions), dash in, yell at your monitor and give him everything you have. In some cases, you will even be able to dive under his tower, kill him (unless he is actually Zilean and had his ultimate, of course), and survive.
However, remember that your choice must not only be aimed at the laning phase, but the whole game. For example, don't pick Shen for the mid lane if your team expects heavy burst damage from you later on.