What are useful tips and tricks for collaborating remotely? What techniques have you found to improve collaboration with a remote colleague, in particular to make it feel more like collaboration in person? 

The majority of my collaborations are with colleagues outside of my state.  The simplest model I've used is that we each write up certain proofs, and then eventually one of us organizes the various pieces into a draft of a paper, which gets passed back and forth via email until we agree that we're ready to submit.  However, this typically feels quite different from collaborating in person.  One technique that I've used with surprising success is to skype with my colleague.  He was actually able to write on the chalkboard so that I could read it.  What techniques have worked best for you?
A good Revision Control!! I use Git coupled with github being an efficient way (and free) to share and complete a collaboration, especially for code and latex files. 

Else, google docs is also free,  allows to multiple persons to edit the same file at the same time, and you see who is doing what. You can do most "Microsoft Word" formats and things. You have also have as service free video-conference and chat.

I highly discourage Dropbox to share files edited per more than one person.