Achievement Progress

For the platforms that support them, in-game achievement progress notifications are a great way of making a game feel more polished and providing feedback on just how much work is left for the player before they will be awarded. This is as opposed to just relying on the platform entirely, so the only information players get about them is via the Dashboard or the XMB with no mention in game anywhere of achievements.

Now, there are a lot of achievements for which measuring progress is not applicable, as it could be for performing one specific stunt in a fantastic and noteworthy way and thus you've either done it or you haven't. But there are also a lot of achievements along the lines of "do thing X for Y number of times". When Y is a significantly large enough number, you can be several sessions into the game before you get it.

Before you do, it can sometimes get to the point where you're wondering why you don't yet have it. "Surely I've killed enough bad guys with the machine gun to get the achievement!" you cry out, but without some indication that you're nearing the target, you don't even know if what you're doing is what you need to do to earn the achievement in the first place!

Gears of War 2 is a great game for progress notification. As well as the "War Journal" in the main menu, that details all of your achievements gained to date and how close you are to those you haven't, you also get in game pop-ups that inform you just how close you are every time you cross a certain threshold.

Team Fortress 2 is similar to Gears with it's in-game notifications as well, but Valve have worked hard on Steam and you can get a lot of information on your achievement progress without loading the game up at all. However it doesn't seem to be consistent.
Browsing my list of achievements, for instance, shows a lot of them with progress bars, quite a few of which are still at 0, such as this one:

Trailblazer
Ignite 10 enemies that have recently used a teleporter.

But then there's this one:

Infernal Medicine
Extinguish 100 burning teammates.

Which doesn't have a progress bar (and doesn't provide any information as to why that might be).

Geometry Wars: Retro Evolved 2 is an example of a different way of doing achievement progress.

The "Wax On" achievement description is "Rub your ship along all four arena walls in pacifism".
To show the player's progress, the game highlights the parts of the wall that have already been touched - that way the player knows for certain what is left to do to earn the achievements.

You can see an example of this in the video (you may want to mute it).