Free to use unless otherwise noted!
Evernote: Take notes, brainstorm, keep your pdfs in one place so you don't have to find them again. Evernote is the ultimate organizational tool! (Free but $5/month premium version might be worth it...)
Notability: If you like using a tablet, this is your best bet for a flexible note-taking app. Combine type with handwriting, highlight, draw, and record audio. ($1.99)
Skitch: An evernote product and free to use. Known for being able to annotate images but you can also annotate and mark up a PDF. (Requires evernote premium)
Google Docs/Drive: Honestly, I use this the most. Very flexible- like having a low-budget Microsoft office everywhere you go.
Endnote: Not for everyone, but you might be using this in other classes. Keeps all your citations in one place and helps you make a bibliography easily.
EasyBib: Similar to endnote but a bit less comprehensive. One big time-saving tool is the barcode scanner on the iphone to quickly get the citation of a book!
The Purdue OWL: Everything from citations and style to research paper substance, this is a site that even your professors use!
MindMeister: Even with a "Basic" (i.e. free) plan, you can create and share mind maps.
Portland University Assignment Calculator: Are you on track for that gold-star assignment? PU can help!
Workflowy: Create simple lists for everything you still need to do.