My previous institution had/has a football app, which I never used, and that was it. My current institution has a pretty awesome app that has maps, official calendars, course scheduling, library room reservations & hours, a directory, various transportation stuff, summaries of what's happening on campus in the current day, articles from the school newspaper, and a bit more. It even uses the schools new logo, which cost the school more than half a million dollars to design, and which virtually everyone hates or doesn't care about (aside from the absurd price tag merely for the design).
Helpful apps on my iPhone:
-Native voice memos app (so useful for professors who have information packed powerpoint slides they don't provide, and then simultaneously lecture on stuff isn't on the slides they're rapidly changing)
-Native notes app (tons and tons of different lists of stuff I have to do; somewhat redundant with calendar app, but not really because I mainly use the calendar app for reminders)
-Camera app (oh so useful for professors that use an entire board, or better yet, multiple consecutive boards, to construct elaborate diagrams no one has any hope of accurately reconstructing on a comparatively tiny piece of paper)
-Calendar app (namely, the reminders function, letting me know I have stuff to do beforehand, in the event I totally forgot or got wrapped up in something else; also quite useful for scheduling things so that I don't end up double, triple, or quadruple booking my time, which I did "back in the day" before I started using the calendar app. Oops.)
I have too many other random apps on my phone to mention, most of which I use when I have periods of what would normally be unproductive downtime. Random vocabulary flashcards while standing in a line to order coffee? Why not.
Helpful apps on my iPad:
-iAnnotate PDF (I seriously just make sure all of my ebooks are in PDF format, or find ways to convert them to PDF format, so I can use this app to read them. I don't rent textbooks or resell them, given that I tend to use them for reference fairly often, haha)
-Safari & Opera (for the rare cases that Safari isn't quite as suitable) for browsing the internet
-Teamviewer (OK, so no relation to school, but sometimes a server that I run that's associated with a gaming community has somewhat urgent issues that need to be resolved to avoid me getting lots and lots of angry PMs and emails, and this app works wonders to allow me to login to my desktop computer, and use my desktop computer to RDP into the server to actually fix whatever the problem is, if that makes any sense)
-All the stuff I mentioned for my iPhone
iAnnotate PDF is also useful because I promptly scan all paper notes, handouts, and whatever else I get. Makes for easy categorization of stuff, easy finding of stuff, and so on and so forth. (And I don't have to carry mountains of stuff around... Although, I've literally scanned like 2000 pages of stuff for just one course this semester... which is kind of time consuming)
Laptop (formerly a 5-year-old Dell Inspiron 1420 which died, currently an ASUS Zenbook running a heavily modified windows 8, and often running a virtual machine running BioLinux 7 from windows 8, because I haven't yet really bothered figuring out how to workably dual boot given the new boot system):
-Dropbox / other similar services
-the Enthought Python distribution (OK, not really a program or app, but, whatever)
-Notepad++ (for writing code in Python)
-VueCalendar (syncs with google calendar, which syncs with my idevice calendars)
-Actual Window Manager (AMAZING - especially on my desktop)
-More additional programs than I can really list
Desktop (gaming rig with 3 monitors, that I barely use for gaming anymore):
-Same as laptop
For a lot of things, multiple monitors increases your productivity by so much it's almost unimaginable, although there's a bit of an adjustment period. For other things, having a single screen is ideal.