Forgot to mention the other that I've seen:
Mosquitoes (obviously)
Mantis (nasty. Which change colour around their surrounds. One got in the house, darted under the sofa, we picked up the sofa and it has turned cream like the underneath)
Cockroaches (didn't know they could fly....ewww!!!)
Wasps, bees and hornets.
Crickets, locusts, small ziziros (don't know their English name)
Spiders (some are like off a sci-fi movie set)
Centipedes and millipedes (huge ones that are yellow that pack a nasty bite!).
You are unlikely to be bitten by anything other than mosquitoes.BUt Cyprus is a haven for the weird and wonderful...and that's just it's people