I try on some level to never watch the same version twice.  The story varies slightly between them all, so why not experience the variations and give up on the definition that there is one all mighty version which defines a personal canon experience of 'The Star Wars'.

With all the new releases coming out, it constantly changes for me. However, please note that I really don't watch the prequel trilogy often no matter what version. Here's my current list.

1. Star Wars/A New Hope: Tie between Lee Thorogood's 1997 laserdisc preservation and Moth3r's widescreen bootleg telecine. I grew up with the 1997 version and (despite it's shortcomings) it's got a special place in my heart. Though I prefer the original theatrical version, call me crazy but I like the color timing of the 1997 (not 2004) edition. Guess it always looked right to my eyes since that's the first I saw of Star Wars. On the other hand, Moth3r's widescreen telecine is Star Wars in its purest form. Whenever I watch the telecine, I can imagine being a person in the 1970's excited by the spectacle of Star Wars.
2. Empire Strikes Back: Adywan's AVCHD. I'm somewhat neutral about the 1997 changes to Empire, which didn't feel nearly as much as the ones made to ANH and ROTJ, so I simply like the highest quality version. I also love the color timing and look of the lightsabers.
3. Return of the Jedi: Harmy's 1983 Theatrical Reconstruction. Unlike the other two Special Editions, I simply thought the ROTJ SE was god-awful. I also loathed the color timing of the DVD and can't stand the lightsabers. Harmy's reconstruction has brilliant lightsabers, and the color timing just makes everything feel so... right. Note that I'm watching the NTSC DVD5 version with Hairy Hen's 5.1 mix muxed in to replace the inferior 2.0 audio track.
4. Phantom Menace: L8wtr's Shadow of the Sith fan edit. It's much more streamlined and fun than the official cuts. Though if I had to pick a non fan-edit, it would be Adywan's AVCHD since it is the best quality.
5. Attack of the Clones: The Phantom Editor's Attack of the Phantom fan edit because it made the love story less cringe-worthy and more believable. As for a non fan-edit, I would choose the DVD since it's the only one I know of, as there hasn't been a reconstruction of the IMAX Cut yet.
6. Revenge of the Sith: Stankpac's Revenge of the Sith fan edit because it cuts the Yoda battle and makes many alterations that improve the movie. If I had to pick a non fan-edit, it would be the official DVD; though I may like Adywan's theatrical version if I could get my hands on it.

So there you have it, those are my favorite versions. Although to be honest, I expect that by the end of the year, my favorites will change. I'll definitely love Spence's ROTJ edit which looks like a vast improvement of story. I also probably may start preferring ESB: Revisited or Harmy's improved De-specialized editions (if they come out this year).

I feel that, to answer this question, a range of sorts would be a better way to answer.  These are ordered by the frequency I choose each version - #1 is most often, #2 is less, so on and so forth.

Star Wars

1. Dark Jedi's GOUT V1 restoration, usually with the 1977 mono mix, occasionally with the 1985 stereo mix, and recently with Hairy_Hen's wonderful 1977 70mm 5.1 reconstruction.  (I also cropped out the yellow subtitles in the letterboxing, and made my own SRT subs to replace them.)
2. Adywan's "Revisited" NTSC DVD-9
3. EditDroid DVD (if I ever want to see the '81 crawl, that is)
4. Official widescreen 1997 SE VHS (second set, after they stopped calling it the SE)

The Empire Strikes Back

1. Adywan's 1980 Theatrical restoration, either with Ady's 5.1 or Hairy_Hen's purist 5.1 mix.
2. Dark Jedi's GOUT V1 with the 1993 stereo mix.
3. ABC/Dark Jedi's "Imperial Edition" (isolated score w/black-and-white video)
4. Adywan's 1997 AVCHD restoration
5. Official widescreen 1997 SE VHS (second set, after they stopped calling it the SE)

Return of the Jedi

1. Harmy's 1983 Theatrical restoration, with Hairy_Hen's purist 5.1 mix.
2. Dark Jedi's GOUT V1 with the 1993 stereo mix
3. Official widescreen 1997 SE VHS (second set, after they stopped calling it the SE)

The Phantom Menace

1. Adywan's 1999 Theatrical restoration, with the laserdisc 5.1 mix
2. Official widescreen 1999 theatrical cut VHS

Any other versions I pretty simply never watch.  I refuse to ever put the 2004 DVDs in, I have no reason to ever put in the official GOUT discs when I have DJ's restorations, I never have any desire to watch Clones or Sith, and I never have any desire to watch the official DVD cut of Phantom.

I really only put the SE VHS tapes on the list to illustrate what I'm willing to watch before any of those things I just mentioned.

Some interesting versions people have listed so far. What I think is most interesting, is the appreciation of the 1997 SE releases - they seem to be more tolerated than the 2004 SE and I can understand why. For example I liked the enhancements in ROTJ 97SE but could not stand the changes in 04SE version - it just went too far.

The Aluminum Falcon, I find what you say about the ROTJ SE interesting, especially about colour timing. I too thought the 2004 version was just horrible - way too saturated and the Vader vs Luke scenes too dark and muted. In the 1997 version I thought it looked improved over the original in places regarding colour timing.

Puggo - Jar Jar's Yoda said:

When suggesting that the colors in the 97 version were improvements over the original, remember that you're comparing 1997 video against older video versions.  There has never been a decent video transfer of the original FILM using today's video technology. To me, the 97 version isn't an improvement on the original, it is just a better quality copy of the original, with some unfortunate changes.  In fact, watching the 1997 version in the theater was the closest I ever saw to what I saw in 1977 in the theaters, because everything I saw between 1978 and 1996 had degraded.

The ideal version would be a modern high quality copy of the original film, which in my opinion would look better than every version out there today, including the 1997 SE and every fan version.

Well, of course. I have never seen a high quality original print to compare, so on that basis like you say, compared to the other lesser quality versions that currently exist of the originals, I do prefer the 1997SE colours, in one particular film, ROTJ.

If I'm just watching the original films, I just watch the official GOUT. My tv is 4:3 anyhow so the non-anamorphic doesn't bug me too much.

If I'm watching the prequels, it's generally going to be Phantom Edit, Attack of the Phantom, and Spence's ROTS edit. I've seen Stankpac's ROTS edit, but I still prefer Spence's. I guess it might have to do with how Stankpac's feels a little TOO trimmed down to me, maybe.

When I am in the mood to watch all 6 together, it's usually the above followed by ANH Revisited, and then I don't know... never actually watched all 6 at once.

On the subject of Return of the Jedi, I have no issue with the 1997 version's coloring which is a vast improvement over the GOUT's decidedly bland and washed-out colors. However, in my opinion, ROTJ suffers the worst from the 2004 color timing, from the awful lightsabers that went through each other to the sterile, unmajestic, and annoying feel of the too-blue color timing. Even before I found out about the whole color timing fiasco and the original unaltered trilogy, I couldn't bring myself to watch the DVD of ROTJ and would always turn to the 1997 SE VHS, my only other alternative at the time. On a seperate note, I've always disliked the SE of ROTJ. ROTJ was the first theatrical version I watched, and I've always thought that the SE changes ruined it. From the Sarlac to the unnecessary celebrations, I simply didn't like the Special Edition, so before Harmy's edition, I always watched the GOUT. When I eventually watched Harmy's magnificent reconstruction, I was overjoyed since his color timing made everything feel so right, majestic, and epic. ROTJ was now the movie I wanted it to be, with no trade offs of bland color, bad SE changes, or horrible color timing.

Puggo, I also agree with you about the '97 editions having fairly accurate color timing when in theaters. I actually think that the '97 SE color shown in the G'Kar, Reivax, and Flunk release is actually what was intended for Star Wars to look like. Star Wars always struck me as a colorful saga and definitely not the washed out, bland films that the GOUT makes them look like. Your Puggo Grande shows this with it's pretty vivid colors, which were probably more vivid when the print you were working from was first made. In fact, I'm surprised no one has tried a theatrical version reconstruction with the GOUT combined with the G'Kar, Reivax, and Flunk releases (with their awesome colors).

GOUT, but only to see if I'm drunk and/or tired enough to not care how bad it is. Success rate varies.

STAR WARS- ANH:R

EMPIRE- SE DVD (Hardly notice the changes)

JEDI- GOUT (I really hate the ROTJ SE changes to the degree I cant enjoy the movie)

Seeing as we are mentioning the prequels I'll mention my favourite versions of those:

TPM: Ady' theatrical reconstruction. I hated the DVD new additions and colours and Ady's version takes me back to when I saw TPM at the cinema.

AOTC: IMAX version. There was a bootleg copy of the IMAX version circulating around the time AOTC was out which I consider to be the better version but unfortunately no longer have it. 8(

ROTS: I don't really have a favourite right now. I haven't watched it properly since I saw it at the cinema, and have been waiting for the ultimate edit of this movie, as I feel it had a lot of potential wasted. Currently patiently waiting on bobgarcia's "Reign of the Dark Side" fanedit.

Personally can't wait to see if people's lists change over this year with so many preservations,edits and then finally the blu-rays coming out. 8)

I think Adywan´s improved version of OT is the only one I´m intended to watch, though I still like the unchanged versions most, especially Episode VI. 

Updated list, since I now have the preliminary release of DJ's V3 ...

... all 3 movies are DJ's V3.  Ady's and Harmy's theatrical reconstructions are the secondary options after the V3.

IV: Revisited

V: Will be Revisited.  SE DVD for now.

VI: I'm sure it will end up being a personal Revisited/SE mix (Depending on how much Ady changes the ending).