It would be interesting to hear from somebody who has actually done this sort of trip. However, reading about some of their exploits in the mags suggests that
The actual flying is the easy bit; anybody could do it and you can fly around the world with the autopilot engaged. A TB20 could fly around the world in 20-30 6-hour legs, all just sitting there with the AP engaged, tracking the GPS track. With a ferry tank, one could do a lot better. Obviously you need to understand weather a lot better than the average new PPL, but it's no rocket science.
The real problems are logistical. You need overflight permits, and need avgas shipped to various places in advance. Being able to burn avtur makes this part a lot easier.
If done properly and to any kind of schedule (i.e. unless done in say a microlight and with unlimited time) the project is going to be very expensive. Egypt has been reported as costing $hundreds per landing, and the well known heli pilot who flew a turbine heli around the world reported spending US$60,000 (IIRC) just paying his way through Russia. Both he and Polly Vacher did their trips (or most of them, anyway) IFR, and had an IR. She has a JAA IR (G-reg) and he has an FAA CPL/IR (N-reg).
There are various weird issues like needing an interpreter in Russia if flying VFR.
As with the UK, having to be VFR is severely limiting, so an IR and a suitably equipped plane is desirable but probably (if you are a retired person with plenty of time and good funds) not essential. OK, nobody can tell if you are in cloud when en route but if you arrive at the destination above a thick layer you can't possibly pretend to be "VFR"...
Unless you have loooooads of time, you will need somebody back home to run the operation, get permits ahead, book the next hotel while you are on your way, pay for this and that, get the weather, and you need good comms - satellite phones are a must and they will cost money too. In Europe, you could do a lot of it with a GPRS enabled laptop but I don't think this will work very far outside, so other forms of internet access will be needed to get weather etc - or have somebody back home running it and you then phone them up on the sat phone.
One obvious gotcha is if you are on a G-reg and need 50hr checks; you will need to find a JAR145 maintenance company to do them, and jolly good luck with that
So, a G-reg on a Private CofA regime, or an N-reg, is a must. Even then, you will end up breaking loads of (irrelevant) rules on the pilot maintenance front (like a pilot not being allowed to do any wirelocking)
At the other end of the scale, I once met a bloke who did about half of such a trip in some microlight. Spent about 6 months on that, living rough in a tent next to the plane and flying the next leg (which, in a microlight, isn't going to be all that far) when the sun came out. I wonder what he smelled like...
Just a few random thoughts from me.... I've been to the further bits of Europe and have no desire to fly SEP beyond that, due to the avgas problems and the sheer boredom of flying such a distance
and then having to fly all the way back..