Okay, I rotated the tires today, and while the tires were off I had a good look in the wheel wells and all around the suspension. Here is what I found:

nothing
no rubbing
no oil leak signs what so ever...anywhere
no shopping bags on exhaust (had that once on another vehicle, different smell than this)
not the limited slip dif (I don't have one in mine)

I also looked at the belt and there is no sign of wear.
Front CV boots are fine, no rubbing.
Brakes are not sticking, no discolouration of rotors (not a hot brake smell anyway)

I did a search and there are others on here with similar situations. Only after a drive at higher speeds or spirited driving (more open throttle), but no results saying what it is.

 

Do you smell the rubber burning after every drive?

 

Only if I have been driving over 65mph or if accelerating hard a few times (not spinning tires). Basically if you drive it so the throttle is more open than normal for a while you get the smell when you stop and shut it off.

 

Let's bring this thread back. Did you guys find out what the problem was? I have a faint burning rubber smell now. It smells like the belt is burning, but the belt looks fine. hmm.

 

Interestingly I have the same smell. It only happens when I drive the truck in the rain, never in dry weather. 2006 5.4 SuperCrew.

 

Could it be the ac compressor clutch? If its raing you probably have the defroster going? I would look for black material particles around the belts for sure. Just guessing here.