Well the orgmode.org homepage calls out one[1] in particular:
"2010-11-25 Thu: Maybe the times where Org mode could change hard-core vi users into honorable Emacs users are coming to an end? A Vim clone of Org mode is be written by Herbert Sitz, and judging by the videos it looks promising."
I'm the author of that clone. I'm making progress, and it's building up to a fairly nice subset of org-mode, but it's not something that would satisfy any truly hardcore org-mode power user. At least not any time in the near future.
The previous poster complained that none of the Vim plugins that try to mimic or clone org-mode "seem complete". That is definitely the wrong way to look at things. Org-mode is a huge app that's been heavily developed for six or seven years now. In some ways org-mode is probably like Microsoft Word: probably 75% of its users access only about 25% of its features, although many of them access a different 25%.
Why try to develop an org-mode clone in Vim, then? Mostly as a personal project I started for fun. I tried switching to Emacs just so I could use org-mode. Even with Viper and Vimpulse add-ons Emacs felt too clunky to me. I had previously worked on a Vim outliner and I knew that part wouldn't be too hard to replicate in Vim. I decided not to stop there and I've gone on to a lot of other features, although it's a fledgling project. In particular, I need to get some decent documentation done. There are a ton of features in my clone that users have no idea are even there. I think so far most of them (like most org-mode users?) use it mostly for simple outlining.
The Vim clone uses a file format compatible with org-mode and actually calls out to an Emacs server to have org-mode do exports to LaTeX/PDF, HTML, etc. So pure document authoring (as opposed to PIM/task management stuff), is one task that the Vim clone probably can do a decent job of now. Adding footnote support is on the list (there's already a Vim footnote plugin that I plan to modify to work with the org-clone).
"2010-11-25 Thu: Maybe the times where Org mode could change hard-core vi users into honorable Emacs users are coming to an end? A Vim clone of Org mode is be written by Herbert Sitz, and judging by the videos it looks promising."
Haven't used it, though.
[1]https://github.com/hsitz/VimOrganizer