I know of 4 major versions - the original releases, the 1997 Special Editions, the 2004 DVD editions, and the 2011 Blu-Ray editions. The most significant alterations were those done for the 1997 Special Editions. The changes were made for a number of reasons - to improve the special effects; to insert scenes that had been cut for practical, logistical, time-related, or financial reasons; to alter plot points; and to add details Lucas couldn't create/afford when he was making the movies.
As for your specific questions, yes, the lightsaber effects were altered, as were the space battle sequences (e.g., more ships were added, editing was made more fast-paced and dynamic, etc).
Several sources offer lists of all (or most) of the changes, but there are far too many changes to repeat the list here. Here is a list of such lists:
DVD Active part 1, part 2, part 3, and part 4
Rather than listing all the changes, I'll provide Wookieepedia's summaries of when and why each edition was changed.
1997 Star Wars Trilogy Special Editions
In 1997, Episodes IV, V, and VI were re-mastered and theatrically re-released as the "Special Editions." For the re-release, in addition to extensive clean-up and restoration work, Lucas also made a number of changes to the films in order to "finish the film the way it was meant to be" (as Lucas said in a September 2004 interview with the Associated Press).
Many of Lucas's changes for the Special Editions were cosmetic, generally adding special effects which weren't originally possible. Other changes, however, are considered to have affected plot or character development. These changes, such as the change referred to by fans as "Han shot first," have proven to be controversial. The "Han shot first" situation can be generally described as this: in the original release of Episode IV, the character Han Solo shoots and kills a bounty hunter named Greedo, after Greedo threatens to kill him in order to collect a bounty which had been placed on Solo's head by Jabba the Hutt. In the Special Edition of the film, however, Greedo shoots first at close range. Only after he misses does Solo return fire. George Lucas has been quoted in Entertainment Weekly as saying that this version of the scene was meant to be the original, as in the original storyboards (Greedo fires first at Han Solo).
In 2000, this version had box art redesigned to match the Box Art of Episodes I–III except the front of the box was white for Episodes IV and VI while Episode V retained the black used for the Prequel box art. Also the Star Wars logos on Episodes IV–VI used the logo design as featured for Episodes I–III. This was done to create a more uniformed look for all 6 movies.
Special coverage on CNN in 1997 notes that Lucas spent $10 million to rework his original 1977 film, which was roughly what it cost to film it originally. $3 million of that was spent on the audio track for the special edition. Lucas also spent $2.5 million each on Episodes V and VI.
2004 Star Wars Trilogy DVD
In 2004, in addition to an extensive and comprehensive hi-definition digital cleanup and restoration job by Lowry Digital, the original trilogy films were changed once again for their release on DVD. In these new versions of the films, a few changes which had been made for the 1997 Special Editions were removed. Even more changes were made to the films, however. With this release, Lucasfilm created a new high-definition master of the films, which will be used in future releases as well. Its sound mix was a combination of the first SE mix and the original mono mix.
One of the most notable of these new changes includes new footage shot during the filming of Revenge of the Sith of Ian McDiarmid portraying Palpatine, which has been inserted into The Empire Strikes Back, which replaces the original performance (voiced by actor Clive Revill and portrayed by Elaine Baker, wearing a specially made mask) recorded for the film. Another notable and quite controversial change was to a scene at the end of Episode VI, when the spirits of Obi-Wan Kenobi, Yoda and Anakin Skywalker look upon the Rebels' celebration. The original actor who played Anakin in this scene (Sebastian Shaw) was replaced by Hayden Christensen, the actor who played Anakin in Episodes II and III.
The 2004 DVD changes were made in an attempt to make a better connection between the old and new trilogies. The 2004 DVD releases also received John D. Lowry's digital restoration visual enhancement treatment.
2011 Blu-Ray Release:
In 2004, Lucasfilm's then-Vice President of Marketing Jim Ward speculated on future releases: "As the technology evolves and we get into a high-definition platform that is easily consumable by our customers, the situation is much better, but there will always be work to be done."
At Celebration V on August 14, 2010, a version of all six films released on the Blu-ray high-definition format was announced. It was said to include never-before-seen and otherwise unreleased deleted scenes from the original trilogy, although the set did not include the original editions.
Examples of some of the changes*:
The opening titles originally didn't include the words "A New Hope" or "Episode IV"; this was changed. Original; 1997.
Mos Eisley was made busier. Original; 1997.
In the original, Greedo never shot at Han; this was infamously changed to make Greedo shoot first. In later editions, it was further altered so that Han and Greedo shoot more or less simultaneously. Original; 1997; 2004; 2011.
The destruction of Alderaan was revamped. Original; 1997.
When Han chases the Stormtroopers on the Death Star, he now finds far more of them. Original; 1997.
Lightsaber effects were improved. Original; 2004.
Space battles now feature far more fighters. Original; 1997.
The destruction of the Death Star was revamped. Original; 1997.
The Force Ghosts at the end of Return of the Jedi were changed. Original; 2004.
Some scenes in the later editions are completely new:
New shot in Mos Eisley, 1997:
New scene featuring a mobile Jabba - 1997; 2004:
*Note: I have focused mainly on changes made to the first film, mostly for brevity's sake. The links above are more comprehensive and cover all of the movies.