AI
There's a joke in the computational neuroscience community somewhat along the lines of "consciousness is where neuroscientists go to die". I literally saw this happen when I was at the Salk institute as a lowly undergraduate research assistant. Sir Francis Crick was there at the same time, and spent his last 25 or so years in pursuit of a theory of consciousness. I was fortunate (and humbled) to get to talk to him a few times before he passed in 2004, and he was undoubtedly a thinker of superior ability and unbounded curiosity (a pretty awesome combination).Actually there were (and still are) a lot of the biggest names in the field there at the time (including Crick, Terrance Sejnowski (a professor of mine who co-invented the Boltzmann machine* amongst other things), VS Ramachandran). These are all people who were coming at the problem from the biological &| pure science/math side of things (vs people like Andrew Ng, who Sam mentioned, who have a more CS/engineering based approach).No doubt they consistently came up with spectacular theories and very interesting models of how a specific regions of the brain may function. How for the most part they worked was this:1. Come up with a biologically or cognitively plausible mathematical model (many of which were fantastically cool). 
2. Implement and run this model on massively parallel architectures (at the time not quite the level of technological sophistication you see nowadays, so things may have changed a lot)
3. To train, use feedback from EEG (this is what I "worked" on, but they also worked with other electrical signals, MRI and chemical measurements at the level of individual neurons).The biggest progress was made at the smallest level (understanding how individual neurons and small networks work). This was primarily because measurement at this level actually provided useful information. The signal/noise ratio of EEG scalp recordings (which to this day gives me nightmares) was (and is) so terrible that I left the field as a quite disgruntled phd student. Maybe I just didn't have the intellectual capacity, but I never felt like I was working on anything that made sense. This was true for many of my fellow graduate students .. after a couple years, we felt we were doing pseudoscience.Rant completed, I think the CS/engineering approach is more promising: don't worry about the biology or some grand theory of the mind and just try to do something useful. Since computers get more powerful consistently, we'll incrementally be able to do more and more useful things. If consciousness emerges at all, it may or may not appear like human consciousness. We may not even be able to tell if/when this happens, but at least we would be solving real problems in the meanwhile.* http://en.wikipedia.org/wiki/Boltzmann_machine