I actually enjoy all of the cliches that are found in anime, as long as they're not over used or forced in to one series. Picking just one or two was so hard I actually put off doing the card til I had time to think about it. So without further ado, here are my favorite cliches.
The nose bleed It is very easy to use it too much, but when you have characters as obviously perverted as Mutsurini and Chitose it works perfectly and is enjoyable. I especially enjoyed the way that Baka Test went to such great lengths with Mutsurini. The fact that they expected to need an blood transfusion for him at the beach was hilarious. Chitose's nose bleeds at her yuri fantasies worked excellently. Having a twin sister that drooled at her fantasies made it even better.
Fan Service While it has ruined several great series, fan service is the reason I have actually found a few good series. The problem is that it is really easy to overdo it and detract from the plot, or in the case of Rosario Vampire S2, forget the plot and just piece a bunch of fan service together and call it a plot.
So there it is, the two anime cliches I like the most.