Well, what kind of electronica. I know, genres, genres, genres, I hate them too, but you need to know them to be able to communicate with people who use them, otherwise you'll get something like: "Yeh, post-rock! You listen?" "Bwuh? Like, Led Zep! Man, Yeah!"
Well, there's Portishead, which is under trip-hop, but I prefer noir techno.
Porishead - Dummy
Then there's Propellerhead, which I think is Big Beat, but I prefer spy techno.
Propellerheads - Decksandrumsandrockandroll
The Avalanches - Since I Left You is pretty awesome.
But from what it sounds like you're looking for more ambient stuff?
So, for that I second Boards of Canada, pick up Music Has the Rights To Children or Geogaddi.
If you strictly want current "indie" electronica, I'll take that as current "popular" electronica.
So try LCD Soundsystem I guess, or Air, get Walkie Talkie? I don't know as much about current "electronica" as I'd like to.