I've been following some of the work going on in the lab of Ned Seeman, a chemistry professor (and rockstar researcher) at NYU.
I've proposed two theoretical ideas toward experimentation in DNA nanotech:
(1) Building an algorithm to convert a desired 3D shape into a set of sequences of bases (that is, a set of specific oligonucleotides) which self-assemble into that shape. At first I coded up a probabilistic algorithm which seems to work fairly well. After this, I discovered a few connections to some results in graph and matroid theory (prompted by a meeting with Dr. Natasa Janoska), which allow a deterministic and guaranteed optimal algorithm. However, this better version of the algorithm was never actually created, mostly because no one seemed interested in actually doing experiments to test the ideas (which would be the whole point).
(2) A trick for building arbitrary DNA circuitboards. There are a lot of challenges toward this goal, and the idea I have in this direction only deals with one of those obstacles -- specifically, figuring out how to transfer the information of "etching" from a 1D strand of DNA to all the elements of a 2D grid of DNA tiles on which circuit elements may reside. In other words, how can you program a bunch of single strands of DNA so that they self assemble into a 2D grid which is pre-etched with a specific pattern? (I don't want to put the details here because - it's sort of complicated - and because there might be some experiments around it, and I'd rather not give away the idea before it's been tested.)