OK, here's the facts....I am an expert in this field, so you can take this answer as final
1. PS2 - Region locked machine full stop. No US games will work on an unmodified UK PS2. Hardware does work (controlers etc). US games are cheaper (if bought from the right place), and typicaly some 3 months earlier released.
Getting games working on a UK machine depends on the age of the PS2. The traditional PS2 requires a mod chip fitting. Its a bit of a nasty job, and requires around 15 wires to be soldered, and a bit of a fiddly dissasembly of the console itself. I don't touch them myself, far too long a job time for me. Warranty is voided due to a tamperproof sticker. Chip fitting service is around £80 at our local computer fairs (although ive not seen the bloke there for some time now).
Slimline PS2 is considerably easier, whilst it can be chipped in a similar way, it is now incredibly easy for an amateur to modify themselves, and simply requires the top half of the machine removing, 2 bits of insulation tape (yes, you read that correctly) sticking over 2 latch switches (this stops them telling the machine when the lid is opened), then the use of a boot disk which enables you to open the lid and swap to your import disk.
With regard to DVD playback, a multiregion product is available and was given free on the cover of a PS2 magazine a couple of years ago.
2. XBOX (my specialist subject) - NOT Region locked by default. Microsoft left it up to the games companies to decide if they wanted to lock out the games, so technicaly, the machine is not region locked. However, most of the games companies did want their games region locked, so they implement machine region checks on boot up and prevent their titles from loading. There are a small number of US games that will work on a UK machine, but they are very few and far between, so much so, that I cant even think of an example.
Again, hardware like extra controllers is compatible.
DVD playback is locked to the first region you use on it, so if you were to purchase the dvd kit in the US, and used it on your UK machine, it would be locked to region 1 and you wouldnt be able to change it (in an unmodified machine).
To play import games, a mod chip is required : Mod chips are considerably cheaper for the xbox, partly due to the dissasembly of the machine being easier, and partly because the unit cost of the chips tend to be lower. Expect to pay around £40 (thats what I charge) and upwards. Once chipped theres a whole load of "homebrew" software available such as emulators and media players. You can connect it to the pc wirelessly and play divx, mp3 etc that are stored on the PC remotely. It becomes so much better a machine once chipped its untrue....but of course the warranty is voided. There are alternative methods to modifying the xbox. There is a software explot mod, which isnt much use to be honest, and also a "tsop flash", which again isnt much use, especialy if you still want to use xbox live (in which your chip must be able to be switched off - something not possible on these methods of modification).
3. Gamecube - The easiest of the 3 main consoles to get playing imports. Simply pop in a easly obtainable boot disk called "freeloader", wait for the prompt, and then put in the import disk. Simple as that. The price and release margins are more significant on this console, which has been poorly supported in Europe.
Alternativley, if you have a US or Jap machine, they can be fairly easily modified to be switchable between the 2 regions, but not to UK.
On the horizon.....there has recently been a mod chip released for the Gamecube, but details are hard to come by, and ive not done any research into it yet.
4. Gameboy Advance / DS - Not region locked whatsoever.
5. Sony PSP - region locked....no more details known at this time.
Personaly, I have a UK PS2, with just a couple of games....I dont like it whatsoever, very dissapointing machine. I also have a UK and a US Gamecube, and a US Gameboy Advance SP. The machine most used in our house is the chipped XBox.