I'm an intellectual packrat. When my intuition tells me to look into something, I look into it, even if I don't really know why I'm interested, and whatever I find I save. Then, after a few minutes, hours, days, months, or years, I can pick it up again and work on it for a few minutes (hours, days, . . .), and file it away until the next time. It isn't for everybody, but it works for me.
A comparatively recent interest is memetics; longer-term interests include cognitive types and conlanging. Of course they're mutually related; sooner or later, all my projects have a way of converging.
I dabble in numerous facets of mathematics, physics, and astronomy, not least their history, individually and in interaction with one another. (Their history provides excellent case studies in memetics. :-) I'm also interested in the structure and design of programming languages, a subject that consistently bridges the gap between hobby and academic research; in, for example, my MQP, my IQP, my Master's Thesis, my doctoral dissertation... Of course, they're all liable to bridge that gap sooner or later.
Those spare snippets of time eventually add up, and I do have some marginally presentable writings on some of these subjects; here are a few, borrowed here from my surfing page:
Conversely, most of my academic work also qualifies as play; and much of my web surfing qualifies as academic. (On my blurring of lines between work and play, see also the category koan I wrote a few years ago.)
See also my blog, Structural Insight.