Nope, there aren't any. Prone says "you are lying on the ground." I had a houserule regarding crouching (kneeling) in 3.5, which was basically half the penalty of prone, but didn't provoke when moving from prone to kneeling and kneeling to standing. In 4E, you could do a similar thing I suppose.
So something like:
Crouch
- You grant combat advantage to enemies making melee attacks.
- You gain +1 Bonus to all defenses against ranged attacks.
- You take a -1 penalty to melee attack rolls.
- You move at one-half your speed.
- You can drop to crouch or stand from a crouch as a minor action.
And really, with the proposed rules cited above why would I not just go prone vs crouching? I don't see a real advantage to it for the character.
There are no rules for it. You could visualize a character as crouching when hiding, using a low barrier for cover, while fighting an exclusively ranged battle, or whatever. It needn't have any significant mechanical effect, but it might help you decide if you want a given terrain feature to grant cover or concealment or not. (Note, not allow characters to 'crouch' to change the cover or concealment they gain, but just to assume that's what characters getting cover or concealment are doing).
If a character wants to get /better/ cover or concealment than you've assigned to a terrain feature by crouching behind it, I'd recomend you use the Prone condition to model it. That makes it a meaningful decision, and puts it in the action economy.
One of the things the 4e design does also is simply not get bogged down in minutia.