It's basically been said already, but I may as well echo it...
If an animal is threatening my safety or the structural integrity of my home, I will do my best to trap it first. But if that isn't possible, it will be killed. Likewise, if my health (or food quality) is being threatened, I will trap the offending creature, or see that it is killed.
Regarding insects, as a general rule, if I can capture it and release it in an area where it will no longer be a problem, I strive to do that. (I'm not perfect, and will sometimes smack that spider on the wall if it's right next to my bed.) For example, I will try to trap a bee in a cup with a lid and release it outside - IF I CAN. Otherwise, it will be swatted. There are times when "trapping" insects to release them elsewhere is unlikely to happen. For example, if my home has a problem with termites, cockroaches, ants, bees, etc.... then the only course of action is to exterminate.
Now, if I'm outside and I see an insect, I leave it alone. After all, it's in its natural environment and I have no right to kill it or bother it.
I think, as it's already been said, that it has a lot to do with your attitude. I don't think it's appropriate to kill an insect simply to kill it for fun, or spite. That borders on sin to me, because it reveals a heart that is inclined toward cruelty and hatred.
I'm also VERY MUCH opposed to hunting for sport. I DO believe that is a sin. It's not the same as killing for food, which is a necessity. Killing for sport is nothing more than a cruel, sadistic game that humans play. And with respect to killing animals for their meat, I believe it should be done with minimal suffering to the animal. I accept that God allows us to kill animals for food, but it must be done in a humane way.