I just want to burn him at a stake and watch his witch's heart bubble. It’s extraordinary. Great trick. - Stephen Fry

Derren Brown does many amazing tricks - I want to focus here on his "mind reading". This is way beyond any cold reading I've seen, but he insists that he uses no actors or stooges. He's also a skeptic, very clear about not being psychic. He does reveal some of his tricks, but maintains a lot of mystery.

Reading David Frost's mind - unusually, he struggles and gets the first one wrong, and seems to reveal tiny glimpses of his technique. Then at the end he gives more hints about his technique than usual. 

Pet name - getting someone on the street to read another person's mind. In the full version (from the DVD of Trick of the Mind, series one) the segment starts with Derren telling the guy (the pet owner) that sorry, it won't work on you, then later changing his mind and bringing him in.

Creepy clown - the detail here is extraordinary. 

Watch the videos then scroll down, if you want to watch it without being influenced by me... I have a few thoughts, but they don't go very far in explaining it... 

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Whatever he's doing, he's extraordinarily good at it. Some speculations:

• Derren Brown uses suggestion and "subliminal" messages very heavily in his tricks. Often he will have written down the person's choice long before they've chosen, and subtly gets them thinking about what he wants. In the examples above he doesn't have much opportunity to direct the thought, I think... except that in the case of David Frost choosing a place, Frost is looking in the direction of the city scape behind Derren, which presumably influences his choice. 
• Micromuscle reading: When he or a participant tries to read a thought, there's often something about picking up the sound of a letter. Perhaps he reads involuntary micromuscle movements related to the mouth and throat that happen while saying something loudly in one's head, but suppressing it. (I would have guessed that was impossible... it still seems unlikely, but much more likely than "he's psychic".)
• He narrows down the field of possibilities, often through suggestion, or sometimes (as with David Frost) asking them for something more specific. 
• He usually selects the participant, making sure he's got someone suitable. Perhaps all TV show hosts are suitable. (Except in his stage shows, where he throws a teddy bear into the audience, and asks the audience to throw it again. Perhaps if you've bought an expensive ticket to his show, you're invested in it and ready to go along with him, and that's enough for those particular tricks.) He says that a few things increase suggestibility, including the presence of a camera.
• He's extremely observant and good at making connections - in one trick, he tells a man a lot about himself, by holding his hands through holes in a panel, but not able to see the man. E.g. by the roughness of the man's hands, he guesses what sport he's interested in. He pulls his hands back, smells them deeply, then declares that he has terriers (correct - he attributes that to having learnt to tell the difference between breeds of dogs by their smell), probably 3 of them (correct - no idea how). 
• Any of these things might be misdirection. 
• He may be lying, and actually using actors & stooges in some of his tricks. But that doesn't explain everything very well (e.g. I doubt that David Frost, Jamie Oliver or other celebs were paid to go along with him, but again, it's more believable that they're all lying than that he's psychic.)