Is there any advantage to using pedal straps over clipless pedals? Other than not having to buy special biking shoes, is there any clear advantage to using pedal straps over clipless (aka clip-in or step-in) pedals?
The biggest benefit I see is convenience.  You can just hop onto a bike with whatever you're wearing at the time and go.  Not a big deal if you're planning a 15 mile ride, but a real big deal if you're riding around the neighborhood, hopping off to run into a few stores, etc...

It's also possible to pedal on the flip side of the pedal and get moving without the cumbersome and slow start up that is required to get into clipless or straps.  In an emergency you can even stomp on the straps and move the bike out of the way.  It's rare, but occasionally you find yourself standing there and just want to get out of the way, in any direction.

I've now switched almost entirely to riding clipless though.  Between that and riding fixed gear, it makes the bike feel so connected to me.

To compare:
Straps are easier to get into.
Clipless are easier to get out of (really!).
I've never pulled out of my clipless pedals, I have broken a strap (no big deal if you're not in a sprint).

At this point if I'm riding any distance at all, I change shoes.  If I'm just going to the store to pick up groceries, I don't even have straps, just old school pedals.  The middle ground for straps just evaporated for me.