One of the things that I've seen repeatedly in anime is what I call 'disposable first episodes'. The purest form of the disposable first episode is where nothing in the first episode is ever seen again; it takes place in a location that the story never revisits, involves characters (apart from the protagonists) that we never see again, and the events are never referred to or affect anything.

(The most recent pure form disposable first episode that I can remember is the first episode of D.Gray-Man.)

One common pattern I've seen is that a disposable first episode will be used in a shonen action series where the real start of the story has the protagonists looking wimpy or otherwise uninteresting. Here, the disposable first episode serves to have the protagonists show off and exhibit their trademark powers (which they may not use again for many episodes), instead of just having them look unimpressive for quite a while in the main story.

(I can see the appeal of this to the creators; it gives the audience some action to get them interested or to pacify them so that they don't get bored when you start in on the slower bits, like the character backgrounds.)

This was brought to mind by the first episode of Fullmetal Alchemist: Brotherhood, which at least felt like a partial disposable first episode in that it seemed like it was there mostly to run us past a lot of important characters doing their trademark thing in their typical way. Personally, I prefer more leisurely introductions.