Specifically social science nerds, but anyone who likes getting their hands on new information or seeing information in more convenient ways will probably enjoy these. (Selections were chosen based on functionality rather than content--almost all of them use content that's already available on the web.)
All of them are free or have a free version, consistent with a grad student's budget (the iPad itself was a very generous graduation present from my parents). They're posted roughly in order from most to least time that I've spent using them over the past week.
Strengths: Hands down my favorite app so far. Allows you to put your favorite RSS feeds into a format that's a cross between the home page and a newspaper. Some of their ready-made feeds are pretty good (News, The New Yorker).
Weaknesses: I can't figure out how to get more than two pages (21 feeds) in the main section. Sometimes if I check it at the end of the day it seems not to have posts that I know should be there from what I've seen on Twitter (see below).
Strengths: Being able to open tweeted links while also scrolling through my feed has been super convenient. Also, I've started following a few feeds in Spanish and Arabic to brush up on my language skills, and if there's anything I don't understand I can just click "translate" and voila, it's there.
Weaknesses: I don't love the way that the feed just sits in the middle of the screen when you have it in vertical (portrait) orientation. Also if you open up a link on the side, sometimes it doesn't want to be swiped away.
Strengths: My main complaint about having so many PDF's to read in school is that you either have to print them out (gasp!) or keep your notes about them in a separate file (or have Adobe Pro, but how many grad students who aren't design majors have that?). uPad (and another app that I've been shown but can remember to get from the app store) allows you to annotate PDF's as long as they aren't locked. You can highlight, write with your finger or a stylus, or create a text box for typing. When writing/drawing it has a feature that allows you to do it at a convenient large size on the bottom of the screen but the finished text/graphic is a smaller but readable size on the "page."
Weaknesses: There are some functionality things that I haven't quite found out how to do yet but I think it's just a matter of spending time with the app (or perhaps buying the full version).
Strengths: Great visualizations of US health statistics by county.
Weaknesses: There are a few kinks, such as the fact that colors representing low/high are reversed for a couple of indicators). In future versions I'd like to see the ability to overlay/cross tabulate two or more indicators and I would love--love!--if this was made more extensible so that other data could be viewed in the same way.
Strengths: A neat visualization tool that allows you to explore your iTunes library as if it were a solar system. As a song plays, it "orbits" the album that it came from. I was glad to hear that this is the first in a planned series of visualization apps.
Weaknesses: If there's a way to sort by anything other than the usual order of Artist->Album->Song I haven't found it.
6. WordPress for iPad
Strengths: Allows you to view and edit your blog's comments and posts from the iPad.
Weaknesses: This app offers no additional functionality over the iPhone app. I started a post on it yesterday, but switched over to my laptop because it just wasn't convenient to insert pictures or links into the post (using photos already online wouldn't be to hard to insert into the html, but I'm not really eager to do this on the iPad touch screen).
Overall I would say that the iPad has so far been even more useful than I imagined, and has caused me to interact with web content in new ways. I'm following more RSS feeds in Flipboard than I would usually check online in a day. The most interesting change is that I find myself categorizing Twitter into different categories: I'll browse through my timeline or look at photos on my phone, but if there's a link I wait to access it on the iPad. If it's a link with multiple pages of content or something I want to blog about I wait until I'm on the computer.
Bottom line: it's great for accessibility and finding cool things that I wouldn't spend time messing with on the computer, and when school is in session I'll be a lot more likely to take my iPad to campus than my computer. I still need to find apps that allow me to actually generate new content rather than just access existing stuff, though. Comments/questions/suggestions?
[h/t to Flowing Data for recommending Stats of the Union and Planetary]