How slow are you supposed to fish soft plastics?

VERY broad question. There is not one "speed" to fish soft plastics. Completely dependant on conditions, personal preferences, type of soft plastic bait, etc...

Exactly, just depends on conditions and the soft plastic.  If you are using a fluke you are probably going to work it faster to immitate a baitfish.  Worms can be worked a variety of ways.  When using worms I would just say (the harsher the conditions, the slower you will work it).  During the winter, and sometimes in summer, I will totally deadstick a worm.  Some days you can almost use a worm like a jerkbaits and get hits.  Just depends on what they want.  Good thing about this is that its hard to mess a spot up by fishing too fast or slow.  Just try different techniques

How slow are you supposed to fish soft plastics?

Arthritic snail pace sounds pretty slow to me.  ;D

How many times have you gotten a backlash?  A couple anyways if you are like me.  Anyways, ever been fishing a fluke, senko, tube, plastic worm and got one?  So you casually pick out the birdsnest, might take a couple minutes.  Meanwhile your bait is sitting on the bottom of the water, probably not in the spot you even meant to cast.  So you have the problem fixed, reel in your slack line, and find a present on your hook.  Goes to show that we probably fish too fast most of the time.

Well said!

I think it was Paul Elias that said." when you fish a worm slower than you ever have before, slow down a little"  

Ronnie

You can fish a worm to fast but you can never fish a worm to slow  

Yes you can fish a worm slow, but when talking about all soft plastics the speed varies greatly