Best AR15 Modifications for Accuracy?

What modifications have you found most effective for improving the accuracy of your AR15 or its variants?

If it wears an optic such as a red dot or a scope, make sure the base is tight on the receiver and the scope rings are properly tightened. Follow the scope makers guidelines and use a inch bound torque driver.
Yours probably already has a free-float barrel shroud (handguard), but if not, I'd start there.
Make sure the gas tube doesn't contact the upper receiver where it enters.
Check the rifling twist rate to see if it will properly stabilize the length of the intended bullets. Most are 1:7 or 1:8" so that's probably not an issue. Don't worry about over stabilization with lighter bullets.
If the barrel fits loosely in the upper receiver (you have to take the barrel nut off for this) bed it with some thick blue loctite. I don't remember the loctite number, but you can research that.
Trigger: I hesitate to send you too far down that avenue. For field work I don't like anything lighter than 3 1/2-4# triggers, but I'm the outlier in that regard. Timney trigger makes an excellent adjustable one piece trigger assembly. I haven't looked, but maybe jard does as well. If you prefer a more traditional trigger assembly, look for national match type triggers. The trigger you currently have may be fine.
If you hand load, try higher quality bullets such as Sierra match kings or Berger. Hollow points are usually more accurate, but not always. Every barrel has its preferences.
Barrels: If you don't find acceptable accuracy after the above steps and money isn't an object, you might want to look at barrels such as Bartlein, Krieger, etc. if you go that route, treat yourself to a Bravo Company upper receiver. They're slightly undersize, making thermo fitting necessary. This isn't as complicated as it sounds, just put the barrel in the freezer overnight and then warm the receiver with a hair dryer or heat gun to expand the opening. This assures a tight bedding. Don't overheat it, just get it warm enough that you don't want to hold it very long with bare hands. Use a torque wrench to tighten the barrel nut. Don't wear gloves!

I don't know your level of knowledge, so I'm aiming this at the lowest common denominator. Good luck!

What modifications have you found most effective for improving the accuracy of your AR15 or its variants?

All depends on what your AR is and your skill level 

I have a LaRue AR that is stupid accurate and the best thing I did was a case of high quality ammunition and shooting 100rds a day max getting to know the rifle 

but I was also getting tips from long range shooters at the same time

I love my Rock River Arms 2 Stage Varmint triggers- they snap like a glass rod.

There is a lot to be said for lapping the upper receiver face to the barrel extension. You don't want to touch the inner diameter of the upper receiver though, you want that snug. But that front face is never perpendicular to the bore on the mass produced AR. With a lapping tool you can make it so.

But the biggest thing is the barrel. A good quality barrel is the heart and soul of an accurate AR. I've got 2 Black Hole Weaponry barrels and they shoot better than I can. 1 is a 5.56 and the other a 6.5 Grendel and they will both stack bullets on top of each other. I am sure other barrel makers can do the same, just look around and you will find one.

I completely forgot about lapping the upper receiver face!