Moths aren't the only things attracted to the light of a moth trap. I frequently find Ladybirds, Bumblebees, Wasps and an assortment of flies in the trap.
Unfortunately this beetle, which I think may be a Shore Sexton Beetle, has been quite frequent this year. They don't do any damage, but they do smell atrocious. The are normally covered in little mites and are always reluctant to leave the trap.
One group of insects that I know very little about are the Caddis Flies. I don't think that I'd ever seen one properly until I ran a moth trap. I catch quite a number of different species, although I can't identify them, I think the one above might be Mystacides longicornis, it looks quite like a picture I found, but with 190 British species it's a bit of a guess. Most of the adult Caddis Flies are nocturnal and although some may be attracted to nectar most don't ever feed. Nearly all of them grow up in ponds and streams, where the larvae surround themselves with portable "homes" made of sand and bits of debris.
Spider are of course familiar to most people, and despite their reputation, there are none to be worried about in the UK (this may of course change if the climate becomes milder and alien species become established). We already have about 800 species of spiders in the UK, of nearly half are in the very small "money spider" category.