For those who prefer riding your fixed gear bike in sneakers, one of the most popular combinations nowadays seems to be the MKS GR-9 platform-type pedals with clips and (double) straps. The popularity of GR-9 has spread so much that according to recent reports, they're sold out pretty much everywhere in the USA at the moment.
I've used that setup myself and I like it a lot, the only negative points being the fact that since the pedals have practically no gripping surface, they're slippery, especially when it gets wet. Also, since the pedals are not made for double straps, you need to attach the clips with bit longer screws which will hold the front strap in its place. In addition, riding on the underside of the pedals doesn't really work too well at all.
If you're into tricks/freestyle, the last point is important since you want to be able to ride on the undersides too. Lot of people have actually started using big-ass BMX platform pedals, like John Prolly here, and SuperTed here (with Power Straps), for example.
Now, I'm suggesting an better alternative to GR-9s:
Wellgo Mini BMX/DH Platform Pedals, MKS clips & double straps.
Wellgo mini platform pedals are the coolest. They're about one third smaller than normal BMX/DH pedals (still big enough for my US 9.5 size sneakers), not much heavier than GR-9s, MKS clips (attached to the INside of the pedal) and double straps fit nicely and the pedals are good to ride on both sides. Lastly, the pins on the outer edges of the pedals can be screwed off, which should be done on the clip side because it makes it easier to get into the clips. The exact model of the pedals is MG-28, BTW.
Props for coming up with this combo actually go to Konkeli AKA the man with the bloody Pista. Cheers!