In addition to log files (covered in another reply)...
- Database dumps (if you're dumping a database to a text file, how often will it be under 2MB?)
- Data, in general. Tab/CSV text files are still the lingua franca of non-hierarchical data and that will probably never change.
- Code you don't control or haven't refactored yet. OK, we can all agree that a 2MB source code file is probably "doing it wrong." But maybe you don't control it. And even if you do control it... well, you need to edit it to refactor it, right?
That said, I don't think the 2MB limit is a total death knell for an editor. I keep TextWrangler (OSX) and UltraEdit (Win) around precisely because they're good with larger files. If my primary code editor is good at large text files, that's a bonus, but it's not a total necessity.
Crazy, but not out of the question. I use Sublime to edit conflicts in .xcodproj files. These brutally detailed XML files - necessary to iOS/OS X development - can be huge. At my previous job one was 7mb.
Definitely situational but not out of the question. Maybe I want to use my favorite text editor to examine a logfile. 2mb is nothing when it comes to production logs.