dtgreene: Here are my thoughts:
First, there is no reason that achievements need to be tied to an online store.
With that said, there are a few types of achievements, some of which are good, but some which aren't:
1. Unavoidable achievements. These are achievements that, barring major skips, you can't avoid if you want to complete the game. Unless the game is *really* short and hard (I'm thinking TGM difficulty here), it doesn't really make sense to have these sort of achievements, unless they affect something in the game. (These work, for example, in Cookie Clicker where there actually is a benefit to getting achievements, but then again that game has no end.) On the other hand, post-game achievements aren't so much of an issue here.
3. Interesting gameplay achievements. These are the type I like, that involve doing interesting things (or getting interesting things to happen). For example, an achievement for skipping part of the game would work (though the problem here is that, if the skip is not intended or discovered by the developer, the achievement can't appear in the first release of the game). Another would be an achievement for dying in an interesting way, to encourage players to search for deaths (particularly interesting for adventure games and roguelikes, both of which sometimes have funny death messages).
1. Those I find rather inoffensive, more like checkmarks on a progression list. Pointless, but harmless overall. Usually they tie in with your point 4.
3. While getting an achievement for a funny death can enhance the humor of said death, but it oftendevolves into things like: Kill a certain boss with only your fists and only wearing swim trunks, while suffering from every status effect. I could do that, but why? Those arbitrary restrictions seem OK if you want to do a challenge playthrough, but randomly here and there is pure padding for no reason.
