Not dealt with anything really disgusting yet, but bedbugs and cockroaches many a time. Went to a house once and it was crawling with bedbugs. They were all over the walls, the beds, the furniture, even in the electrical sockets. The occupants had bite marks all over their arms and upper body (they don't tend to bite the lower parts of the body because they're attracted to the CO2 in your breath) and apparently the poor kids were the same. We had to remove all their furniture and carpets for incineration then heat treat the entire house (heating to 60°C kills the eggs, which otherwise can lay dormant for up to 6 months until they detect CO2 from a host, then they hatch). The most likely places to pick up bedbugs are hotels and commercial airliners. Some of the more expensive hotel chains are infested (not naming any names) due to the large throughput of international travellers.
As for cockroaches, we have native ones for sure, but also German, Japanese and American species. They're bastards to get rid of as well because their eggs can lie dormant for a couple of years.
To date, the most disgusting thing that's happened to me personally was in an office where they had reported nasty smells. Sure enough, the place stank of dead rat. I lifted up one of the ceiling tiles and got showered with rat shit and maggots, then the remains of the rat itself. Lovely. Then I had to clean it all up...
Hornets are fun as well. I'd never seen hornets before last summer - I got a call to treat a wasps nest at an army barracks and when I got there it was a fuckin hornet's nest. Man, they're huge (about 2 inches long), and the most intimidating insect I've ever seen, but luckily not as aggressive as German wasps (they're the ones that build nests in holes in the ground and sting you just for fun). I got suited up and approached the nest slowly. When I was about 3 feet away, several hornets walked out of their nest in the roots of a fallen tree and just sat there glaring at me. Then I heard a loud droning noise and a group of hornets appeared from nowhere, flying in perfect formation, and stopped in a line a couple of feet in front of me and just hovered there in a really menacing way, while making a noise literally like a squadron of B52 bombers. It was one of the most intimidating experiences of my life as I didn't know whether they were going to attack. Even though I had a suit on, it was only the top half and I've had wasps get inside it before - which is a right laugh I can tell you
But strangely, they allowed me to attack their nest without attacking me - probably cos I look like a right 'ard cunt - and soon broke formation to go help their fallen comrades. It saddens me to kill creatures like that (i don't enjoy killing anything, but sometimes it's a necessary evil - like war), because they have such an amazingly organised and complex society that they must surely be sentient, yet in a way that is totally alien to us mere humans. I've not yet been stung by a hornet, but there's always a first time, and I believe it's not a very pleasant experience...