It seems that to many people here have become anti Blaine-style. I don't have a problem with walking up to strangers and performing for them. That said, I enjoy performing close-up table magic a LOT more that I enjoy Blaine-ing, but I still do get to perform magic and there are many more opportunities to perform for random strangers you meet than to sit at a table and whip out your set up cups and balls (my favorite effect

).
I find that approaching random people gives you a great chance to try new things out and get performing experience. If something goes wrong, who cares? End the performance and leave. If something goes wrong in a close-up performance, you could be in a bit of trouble.
The biggest reson I do Blaine-style magic is because it is fun and I enjoy it, though my presentation is nothing like Blaine's (I actually talk to the spectator and tell a few jokes). If you are an experienced magician who isn't shy and have never try it before, do it sometime. You will find it fun.
As for how to approach people, there are a few things to keep in mind:
1. People might say "NO!" and walk away. As someone pointed out, you don't have a camera crew following you around, therefore, you don't strike anyone as being different form anybody else.
2. When approaching people, ask them if they have a moment. If they don't, leave them alone, if they do, pull out you cards, coins or whatever you intend to perform and ask if you can show them something (yes, this approach is very Blaine-ish, but guess what... it works). DON'T ask them if they would like to see a magic trick. This will almost guarantee you a "NO!"
3. After saying "Do you have a minute?" and "Can I show you something?" you will probably be looking at someone with a very strange and confused look on their face (how would you feel if you were in the middle of a public place and someone came up to you asking if you would like to see something). Don't let their confused look scare you away. It generally means they are currious to find out what you are going to do. Take advantage of this and ask them to hold the coin or select the card and begin you performance. You will hardly ever run into the people who agree to see you effect with a huge smile on their face and a excited "Sure!" (you know, like the ones on T.V.). this is because of you lack of fame and camera crew. Your job is to leave them smiling after the performance.
4. Have a routine worked out (a serries of effects that follow each other up nicely). If someone sees you first trick, hands you your card back and walks away, regardless of how much he likes it, DON'T FOLLOW HIM!!! If you do follow him, you will be seen as someone who wants something from him (a possible pickpocett, etc.)
5. Make your effects short and to the point, with quick climaxes that hit hard. Don't whip out long routines that gradually build up (Oil and Water, etc.) If you do and ambitous card routine, don't make it too long. I find that the strongest effects are the type that happen in the spectator's hand.
6. Make sure you can perform the effect under any conditions. Don't bring effects that require a table. Also, don't bring big, awkward effects. I like everything to fit in one pocket.
7. This one might be obvious, but, if you vanish an object of the spectator's, or change it into something else, MAKE SURE THEIR OBJECT REAPEARS!!! You want to be seen as a magician, not a criminal.
8. Finally, be relaxed. The more relaxed you are, the more relaxed the spectator will be. Slip in a few jokes to loosen him up.
You should also know which people to perform for. Here's a basic list of how to find someone who would make a good spectator.
Good:
-Someone who seems to be waiting around for something.
-Someone who seems to be in a good mood and is enjoying their surroundings
-ANYONE you hear talking about what Chriss Angel/David Blaine just did
-Someone walking with a slow, relaxed stride
AVOID:
-People in a bad mood
-People walking quickly (in a hurry)
-Kids 12 and under (unless they are with their parrents)
-Anyone holding a lot of items
Basically, try to put yourself in that possition and think "If I was him, would I want to see a magician (of coarse, you must put yourself in the shoes of a layman).
That's my two cents (or pence for you British folk

)