Good news for everyone who wants more account-wide features, as opposed to character specific!
Most achievements will be account-wide
-This means you only earn the points once. If you have earned an achievement on one character, you can see it on all your characters.
Most criteria will not be account-wide
-If you start an achievement on one character, you can't then finish the achievement on another
There will be few achievements that are account-only
-Only a couple achievements will be account only; meaning that you probably will need more than one character or
will need more than one character. An example would be, "reach level 90 on one of each class" or "get 250,000 honourable kills".
Rewards granted from achievements (pets, mounts, titles, and tabards) will be shared at the account level
-If, for example, you earned a Violet Proto-drake on character A, character B will also have access to it! That way you will be able to use rare mounts and rewards on all your characters, and won't have to get it again.
Please keep in mind that none of these are confirmed, but we can confirm that this is what Blizzard intends to do in Mists. I think that these would be nice changes, so that you won't have to grind on more than one character, and you won't have to feel inferior on one character more than the other just because of achievements earned on it.
You can read Ghostcrawler's full article
here.