The Wampa Attack
Early in The Empire Strikes Back, the original script called for a scene where a wampa busted through the wall in Echo Base wreaking havoc on the base. The scene was cut because of the trouble involved in making the wampa in 1979. Lucas was not happy with the way it came out.
The Bacta Tank
While Luke was in the bacta tank, Leia, Han, and Threepio were originally standing behind a window looking into the room. The scene was changed for the final film so that they were in the room with the tank.
Advanced Healing Bandage
Originally after Luke got out of the bacta tank, he wore an advanced healing bandage over his face. This was probably cut because it may have been frightening for young children.
The Wampa Room
There is a scene when the snowtroopers are chasing Han, Leia, and C-3PO to the Falcon that never made it to the big screen. While lagging behind, Threepio passes a door that has a sign warning people that there are wampas inside. He pauses and then goes to the door and rips the sign off. When the snowtroopers come around the corner, they march heedlessly into the door. Part of this scene did briefly appear in the trailer for The Empire Strikes Back.
Kiss on Cloud City
While in Leia's suite in Cloud City, Han and Leia share another kiss (or near kiss). This probably took place before Chewbacca came in with the dismantled C-3PO.
Luke and Leia in the Recovery Room
There was a scene while Luke was recovering from his bacta treatment where Leia comes in and Luke reveals his feelings to her and they almost kiss. Luke explains how his near death with the wampa made him think about things. Threepio and Artoo spoil the moment and instead Leia tells Luke about the wampa attack (that was also cut). Luke then tells her that he needs to go away for a while. Leia reacts angrily by saying, "First Han, now you-when am I going to learn not to count on anyone but myself." She adds that she was getting along just fine until she met the two "moon jockeys." Han then comes in and the scene progresses as in the final cut. Without this, it is easier to believe that she later kisses him to make Han jealous.