Oh yeah, it's completely irrational, like my other old phobia (bees). I know that I regularly experience worse pain than a needle, or that bees usually don't sting unless provoked, I'm not allergic to them, and there's the pain comparison again, but I used to be completely adamant about not having anything to do with either of them. Nowadays, I'm...well, still not great with either of them, but I can manage.
Wasps, heights, and arachnids are my primary fears.
Wasps: Irrationally, I avoid these things like the plague. I'm not allergic, but I've never been stung before (and the thought of it actually happening is what frightens me most). If I see one, I keep my distance.
Heights: Ironically, this is caused by my own personal height. Everything seems much different when you look down at it, and it only sinks in just how high up you really are when you put it in perspective. I can't fall without nearly pissing myself in fear, and airplanes are a nightmare for me (take-off and landing only, the actual flight is rather pleasant even with turbulence). And yet, I love coasters and I've always wanted to go hang-gliding. But the feeling of my stomach leaping into my chest during a drop is what does it. That feeling makes my nerves act up and forces me into the whole "I'm gonna die!" mindset. My psychiatrist says this is what a minor phobia is.
Arachnids: I've had a habit of killing spiders since I was young. I won't let them near me unless I'm going to kill them. It started because I learned just how venomous scorpions really are first-hand (despite the fact that they are my favorite non-mythical creature, I've been afraid of them for almost 2 decades now), but even the non-poisonous spiders startle me.