Via Arnold Kling, I came across Tyler Cowen's list of five strands of libertarianism: (1) Cato-influenced; (2) Rothbardian anarchism; (3) Mises Institute nationalism; (4) Jeff Friedman and Critical Review; and (5) "Hayek libertarianism."
The list strikes me as a bit odd. The Rothbardian and Mises Institute strands strike me as basically the same thing (and "nationalism" seems a misnomer for the latter), and there seems to be a good deal of overlap between the Cato-influenced and "Hayekian" (not sure why that's in quotes) strands. As for Jeff Friedman and Critical Review, they don't impress me as very important, though that may reflect some (rational?) ignorance on my part.
One could come up with a simpler categorization scheme (e.g. "hard" versus "soft" libertarianism, distinguished by their radicalism or moderation) or a more complicated one (with say left-libertarianism and conservative fusionism as categories). But however you slice it, libertarianism means a lot of different things, many of them mutually incompatible.
For my part, I want nothing to do with Cowen's strands 2 and 3, but think 1 and 5 have much to offer (especially if they don't succumb to getting entangled with strands 2 and 3, as Reason magazine did for much of last year with its ill-considered touting of Ron Paul).