Which AES modes can decrypt from anywhere in the ciphertext
The practical answer is that you should almost certainly be using authenticated encryption, in which case authenticating an individual encrypted message requires you to process all of it anyway.  Once you throw in this element, random access into encrypted data becomes not a matter of message encryption modes, but rather of how to split your data into a collection of messages that you can encrypt and authenticate individually.

The literal answer is that among the classic confidentiality-only block cipher modes, CBC and CTR can start decrypting from any block, while CFB and OFB cannot.  You can read this pretty straightforwardly from mode diagrams; here's CBC decryption (diagrams from Wikipedia entry):



Neither of the inputs to each block cipher call require the output of any other other block cipher call—there are no arrows going outside of one block cipher decryption box and into another, unlike for example with OFB mode: