I think it's kind of an interesting question, that also made me think about the OOTB apps (some are kind of app/hardware) on an iPhone:
Browser, Email, Messaging, Music, Video, Photos, Camera, Contacts, Reminders, Calc, Weather, Stocks, Notes, Calendar, Voice Recorder, Notes, Compass, Maps ...
It really does a ton of stuff with only OEM apps (especially when you factor in a really solid browser like Safari). I think it would be a fun 30 day challenge to use your iPhone, stock apps only
Many of my apps are alternate UIs for existing web based content like IMDB, Facebook, Twitter, DropBox, Amazon, Wikipedia ... so those could all still be used, though with a less optimal front end. Some services would be stinkers like Podcasts (having to stream through a web front end vs. downloading/sync'ing content), but still doable.
I guess a couple of major things I'd miss would be books (since all eReaders are a need-to-be-installed app) and though it's more for my iPad, a good text editor.