I was going to write a very long post detailing my thoughts on 4e, but then I read this really good post which mostly reflected my own experiences. Kudos.
I'll just add a few observations:
* I love the way classes are balanced against one another. In my experience, in 3e fighters were good until about 5th level; casters were good from about that level on, well played caster at all levels. Also, in my view, non-casters followed a linear power curve, casters an exponential one. Put these two things together and you had a titanic power difference between classes which forced DMs to use wonky solutions to make players feel useful (i.e. anti-magic zones, et al) which made encounters unfun for some players. A solution appeared in the form of Bo9S (which I absolutely loved), but that just drew cries of power creep. Thankfully this is fixed.
* 3e can be used to make very cool plot-centric campaigns (I've played in more than a few), but you have to take into account that characters are going to go up in power very quickly. I tried to run a campaign where the characters stayed at the same power level vis a vis the campaign world (the world levels up with them) and it epically failed. I've found that the tier system coupled with the flattening of the power curve allows me as a DM to make a campaign the way I like it (If I want a heroic campaign, I make a heroic tier only game).
*The de-emphasis on system mastery. One thing I found in my group is that depending on the DM, the game was going to favor either optimizers or people who thought character weaknesses made for flavorful characters. If it favored optimizers, non-optimizers felt useless, and if it went the other way around, optimizers felt restrained (guilty). Now nobody in the group feels useless, and optimizers can concentrate on tactics and party optimization, which benefits everybody.
*Combat Powers let me add a mechanical effect to what I am imagining my character is doing, which encourages my combat narration.
* Dynamic terrain is a must. It adds to the gaming experience and lets some powers really shine in some situations and other powers in other situations. Not to say the same wasn't true in 3e, but it is moreso in 4e. Flat terrain is boring in both games.
*One of the greatest additions i've seen to combat enjoyment is minions. It adds a very cinematic element that has really shined in the games i've seen it in.
*I've had no problem as far as non-combat abilities are concerned, because it's always been my opinion that most of them should be relegated to roleplay and character background. If your background says you were a good baker before you started adventuring, you should be able to make good rolls without having to sacrifice skill points that should have gone to adventuring skills.
*I love the way skills have been streamlined, especially the 1/2 level to every skill. 12th level paladins (2+int skill points, Knowledge: The Planes not a class skill) who've been battling demons their entire careers should be able to know more about them than peasants who've never left the dirt farm without again sacrificing precious skill points to be able to do so.
Again, these are my observations so YMMV.
It's better to say that 4e appeals to people who used 3e and found that it wasn't the right tool for their job.
QFT.