Worse than Android apps, it only runs Chrome apps. Possibly NaCl is supported, I've no idea, but the bulk of the apps are HTML/CSS/JS zipped up with some metadata. I've been tossing around the idea of getting a Chromebook, but only if Linux could be installed on it easily, which it seems like some Chromebooks cannot do. Mostly they seem to support a weird dual-install that boggles my mind and seems really sub-optimal. Perhaps someone with more experience can elaborate.
Personally, I doubt I could do very much work in ChromeOS itself, and what I could do would be limited to whatever the "SSH client" in the Chrome store can support. SSH is nice and all, but I'd rather not be stuck doing absolutely everything in it especially if network conditions aren't so good. Nothing like your ssh client lagging while you're trying to edit text. Where or where will the cursor be when it catches up, and what got fucked up in the process?