RETURN OFF THE JEDI
The Rancor pit.
In an effort to escape, Luke uses the Force to jump up to a grate above, but he is unable to get out and has his fingers mashed by Jawa gun butts for the effort. He then drops down right onto the Rancor's eye, causing it great pain... but again ends up on the run.
There seems to be no particular reason for this scene being cut, other than for time or because of the difficulty of the special effects regarding the fall onto the Rancor. It would have given another chance to see Luke exercise his Jedi abilities as he makes the jump to the grate.
A single photo from this scene has appeared in the Return of the Jedi storybook, and the scene is included in the novel as well.
Barge Fight
On board Jabba the Hutt's barge, Threepio has found himself an unwilling translator/mediator between a drunken Ree-Yees and Saelt Marae (aka Yak-Face). Salacious Crumb joins in the fun as well. The altercation ends in fisticuffs, just before Threepio bumps into Artoo serving drinks.
This was just a little extra action taking place aboard Jabba's barge, but it was cut from the film as it was non-essential to the storyline.
Pictures from this scene show up all over in various places, including in the photo insert from the novel. Also, the scene is described in the novel, but it is Ephant Mon rather than Saelt Marae who gets in the fight there.
The Sandstorm
Perhaps Jedi's most famous deleted scenes, after Jabba's barge explodes, our heroes rendezvous once more before taking off and going their separate ways, but they end up having to struggle through a tremendous sandstorm to get to their ships. Chewbacca has been wounded during the battle, and is hobbling along with the help of Luke and Lando. They reach their ships and prepare to part, exchanging feelings and farewells.
This scene would explain how everyone got on and off the planet. Parked out in the desert here is the Milennium Falcon and Luke's X-wing. The script also mentions a two-seated Y-wing being there as well.
EMPIRE STRIKES BACK
Dead Tauntans
We see here that the Tauntauns have been attacked by something, but we don't know what it is quite yet. This is not long after Luke has been attacked in the wasteland by something unknown as well. Han takes little note of what has happened here as he is too busy worrying about Luke.
This was part of the whole Wampa storyline that was trimmed from the film. A tiny bit of this scene is left over in the film: we see a dead Tauntaun on the floor, but we don't get any mention of what happened
Wampa Attack
Perhaps the most famous cut scene from Empire, Artoo-Detoo narrowly escapes as a Wampa Ice Monster crashes into the base, enraged by his electronic whistling. A group of Rebel soldiers only manage to stop the creature with a blast from a large bazooka weapon. Right after this, sensors pick up a new intruder (which happens to be an Imperial Probe Droid).
This is part of the Wampa sub-plot that was deleted from the film. Some of the Wampa footage was filmed, but most of it was scrapped due to problems with getting the Wampa to look right.
Wampa Trap
A number of Wampas have now been captured and are now being kept in a confined area. Threepio and Artoo-Detoo are discussing how the creatures were captured by using electronic whistles like Artoo's. This leads into another deleted scene, which comes later.
Again, this is part of the Wampa storyline that was deleted.
Troops Meet Wampas
Imperial troops have now entered the base, and our heroes are in retreat. But Threepio makes a quick decision to help throw off the pursuers: he tears the warning sign off the Wampa trap! The unsuspecting troops then enter the unmarked room, unaware of the fate that awaits them there. Afterwards Darth Vader enters to find only the remains of his troops.
This was cut since it was part of the Wampa storyline that ended up being dropped from the film. Originally it gave Threepio the chance for a clever but deadly joke at the Empire's expense. It also explains why he was so far behind the others when they ran into the hangar to board the Milennium Falcon. One of the trailers for The Empire Strikes Back actually contains a few seconds of this scene.
Hopefully there will be many more scenes that we have never heard of.
I for one cannot wait to get my copy.