I'm actually quite fearless in terms of watching anything. After being scared shitless with 'scary' FPS like Wolfenstein 3d and Doom when I was an impressionable child with a vivid imagination, nothing really fazes me now that I'm an adult.
Well, I'm fearless apart from shows I have been spoilt or have a big inkilng that the childhood friend couple would lose, but that's for entirely different reasons. Good thing though that I watch anime as it gets fansubbed, so being spoilt is close to none apart from those shows that are adaptations of another work.
Now as for the latter (having a big inkling), I can't help much about since I unconsciously read beneath the surface over anything I watch. All that said, it really isn't as bad as it sounds, as anime has a very good track record with this coupling, and as such these 'inklings' are just uncommon. But for those that I have misgivings (for example, 5cm/s, since Shinkai was never the jolly fellow), I'm deathly afraid to watch for being too emotional about it, either through extreme rage or depression.