Believe it or not, "Which edition of D&D should I play?" is probably the most common question I'm asked. In some cases it is because the person asking the question wants to argue with my choice, but most of the time the questioner seems to sincerely want my opinion. Unfortunately, I can't really answer the question -- because there is no "one true answer." The best edition of D&D is the edition that best fits your needs. The answer for me may not be the answer for you as what you and your group want out of your game may be much different from what I want out of my game.
That said, I will list the various editions of D&D in the order I personally rank them based on how well they meet the needs of the types of games I like to play in and run. Your list may be much different than mine -- and that's as it should be. There really is no one best edition for everyone. Those who tell you there is are probably trying to sell you something.
1) Original Dungeons & Dragons with the Supplements: Fairly simple rules with a lot of room to make the campaign and the game your own with house rules. OD&D with the supplements is a lot like playing AD&D but without all the complex stuff AD&D added. Combat is fast and abstract -- just the way I like it.
2) BECMI Boxed Sets/Rules Cyclopedia: The Rules Cyclopedia (The BECM boxed sets in one hardback book) is probably the best version of D&D ever printed in hardback. It is a complete in one book, well-explained game that one can play for years without much modification, yet it is simple enough to easily house rule to fit your own group and campaign. Like OD&D, combat is fast and abstract.
3) Moldvay/Cook Basic/Expert Boxed Sets: Later expanded into BECMI, this earlier edition only takes characters through 14th level. That is its only major disadvantage compared to the BECMI rules, but it is a great set for those who prefer low level play.
4) Advanced Dungeons & Dragons (First Edition without Unearthed Arcana): If you want more complete rules to reduce the amount of GM rules decisions, First Edition AD&D is the way to go. Compared to later editions, it is still rules lite, but it is much more rules dense than previous versions and has a number of rules designed to better balance character classes -- although not is the same way people seem to see "balance" today. Combat is more detailed but still abstract and fast.
5) Advanced Dungeons & Dragons (Second Edition -- Core Rules Only): This is a cleaned up and slightly simplified version of AD&D, it really isn't all that different from first edition, but it lacks the character of Gygax's writing (which is a bad thing in my eyes, but is a good thing to some).
6) Advanced Dungeons & Dragons (First Edition with Unearthed Arcana): All the advantages of first edition with some extra classes and spells. Unfortunately, some of these extra classes turned out to somewhat overpowered.
7) Advanced Dungeons & Dragons (Second Edition -- Plus the Kit Books): The kit books basically add a large number of subclasses to each standard class. This provides a lot of mechanical variety in characters at the cost of extra complexity and having to buy a large number of rule books.
8) Advanced Dungeons & Dragons (Second Edition -- Plus the Kit Books and the Skills and Powers Books): The skills and powers books add a great deal of complexity to AD&D. They also start the trend of needing minis and battle mats to play out the complex and slow combats. As I like fast and abstract combat and am bored to tears at combats that take more than 10-20 minutes max to resolve, this is where D&D and I began to part company.
9) Dungeons & Dragons 3.0 This is the last edition of D&D that really feels like the D&D game I started playing in 1975 to me. While there were a lot of changes and additions, all the basics of D&D were still there and had not changed so much that they were something different with the same name. Combat is slow and tactical, it's hard to run without minis and battle mats. The designers tried hard to make a rule for everything and to reward players who mastered the manipulation of those rules. Not my cup of tea. GM prep time is unreal if the GM cannot or will not simply wing it. Houseruling can be hard as the game systems are tightly interrelated, changing something can have expected side effects in other areas of the game.
10) Dungeons & Dragons 3.5 Lots of changes to spells and other areas: the names are often the same but the effects can be completely different. Minis and battle mats become almost required and combats are even slower. GM prep takes even more time, but there is a rule for almost everything any character to ever want to do scattered about the many, many volumes of rules.
11) Dungeons & Dragons 4e IMHO, this is a tactical minis skirmish game with roleplaying interludes between the battles given the D&D label. It has very little in common with any previous edition of D&D besides names. 4e character classes and monsters are extremely well-balanced for combat -- and if that is what is important to you, D&D 4e is probably the only edition you will want to play. However, it's not for me at all.
[Don't forget that rare Traveller fanzines (Working Passage & Imperium Staple) and the RPGA limited edition AD&D Modules R1 (To the Aid of Falx) and R2 (Investigation of Hydell) are available (for Cancer Fund Donors) -- addition to the usual PDF downloads every donor has access to. There is still plenty of time to make a donation and get in on the giveaway which ends at the end of October 2009. Thanks much to those who have already donated.]