One of the main things I like about 4th Edition is the refinement of the challenge rating system. I find the encounter balancing system to be easily understood, which makes making combats a lot easier. With the experience points budgets and encounter levels, it is very easy to understand the estimated power level of the party versus the difficulty of an encounter. It gives you very good control over how much you challenge the party.
Format. I love the format of 4th Edition, the way stat blocks are laid out and written. I find the class blocks to be informative and concise, far more easily understood than other editions and their endless sprawls of text. Powers are laid out very clearly. The way they breakdown the targeting and timing mechanics of each power are very nice and easily understood. I guess a lot of what I love about 4th Edition involves how easily understood stats and such are, they really work hard to convey info in well designed blocks and such. The feat format is well designed as well, they're broken up by tier and sometimes by race and class, which can save a little bit of time by showing you directly where to go for feats, rather than having to have to page through all three thousand feats.
I think defenses are a cool concept. One of the design ideals of 4th Edition is to put the issue of success with a d20 roll on the attacker. Like your AC, your Will or Reflex defense is something you control with your stats or feats, and the enemy has to meet or exceed it. I also enjoy that they've allowed you to use the best of your Strength or Constitution for your Fortitude defense, Intelligence or Dexterity for Reflex, and Wisdom or Charisma for Will.I know that it is basically a new version of the saving throws we've had forever, but I do like that they've made it so that the instigator of an action has to make the d20 roll. I also enjoy that defenses have a static number, you're not relying on luck to protect your from an effect that is going deal two hundred damage to you in a round (i.e. Finger of Death), your defense (or that of your enemy) is what it is and you (or the enemy) must work to shore it up and can use effects to improve your chances of affecting your opponent's.
Static hit points. Brilliant, enough said. Your Constitution still has an effect on how many hit points you, but you don't have massive differences in survivability like you can in rare cases with other editions.
I think the design behind the skill system is pretty grand. Many skills have been folded together with others to make some skills more comprehensive. Perception now covers both visual and aural detection and that sort of thing. There has been some oversimplification of the system, but I can get over that. The trained static bonus combined and the 1/2 level bonus system of 4th Edition, really combine nicely to make a very simple and easily understood/used skill system that doesn't end up being some overbearing system of accounting and book work. (A note, I never felt that way about 3.5 Edition and do not feel that way about Pathfinder).
The power system has some appeal to me, but it is a kind of mixed bag. Encounter and at-will powers for martial character represent a sort of suite of maneuvers and techniques learned over years/levels of engaging in battle. At-wills for spellcasters represent orisons and cantrips and such fairly well. In theory, the power system is basically just a different version of the Vancian system of magic, spellcasters are still fundamentally limited in what kind of shenanigans they can pull off, the limits have changed to once a day and once every five minutes, rather than by how many times they memorized something, but they are still limited in a similar fashion to previous editions. Like I said, mixed bag, I like some of it, and other chunks of it bother me. Overall, I think it is a positive. One thing I very much like is that even wizards have to make attack rolls now and that all stats can be used to make an attack roll and every ability score has a use, some affecting the secondary affects of powers. Granted, attacking with Intelligence or Charisma is a bit...odd, however, DnD is rife with dissociative mechanics and attacking with your Charisma bonus is no different than having two hundred odd hit points and having to be stabbed a hundred and fifty times by a goblin to finally croak.
So there's some stuff about why I like 4th Edition, I'm sure I could come up with a few more points, but those are the major ones.