Study Apps

Audiotorium ($6.50)
or AudioNote ($5.50)
Both programs record lectures while you take notes. They have different ways of keeping track of the lectures - Audiotorium has a bookmark feature that allows you to mark interesting points in the lecture. AudioNote syncs the audio recording to whatever you were typing at the time. Click on the relevant point in the text and it will play whatever was recorded when you were typing at that time.

Both allow you to group your notes into different subjects and folders. You may have to sit fairly close to the lecturer though, because both programs use the iPad's in-built microphone, which is not very powerful.

Audiotorium screenshot

Both programs also continue recording even if you exit the app, so you can check email or open your calendar during a lecture without missing a single word from the lecturer.

AudioNote screenshot

Blue Yeti Snowflake portable microphone ($40 from bhphotovideo.com)
So if you choose to use an audio note taking program, you might need an external microphone to give you clearer audio recordings. This one is portable but you will need to use it with the USB camera connector kit for the iPad ($30 from Apple stores or Dick Smith, JB, etc).

Snowflake portable USB microphone

TextExpander
This allows you to create your own typing shorthand on the iPad. For instance, I use it for court reporting to quickly type legal jargon - so if I type "fhm" then I get "forensic mental health report". You can also use it for commonly-used phrases, such as "on my way" or "thanks for your email". It makes typing much faster, especially in lectures. Just be careful to choose shorthand combinations that aren't likely to be used when you are typing normally - I once chose "doc" as  shorthand for "document" but then found I couldn't type "doctor", "dock" and heaps of other words beginning with "doc".

Snippets in TextExpander

Evernote (free but you pay for extra space in your account)
Some people love this and some people hate it. It's an "all in one" app that allows you to take notes, clip pages from the web, draw sketches, add photos, maps and diagrams. It organises everything for you and is supposed to help you "remember everything" but it's also quite a big program with lots of features to remember. Still, many academics swear by it.

Evernote

 
NeuAnnotate (free)
This app allows you to highlight, mark and make notes all over a PDF file, which is really useful if your lecturer puts up lecture notes in PDF format.