fugitive.vim
I'm not going to lie to you; fugitive.vim may very well be the best Git wrapper of all time. Check out these features:
View any blob, tree, commit, or tag in the repository with :Gedit (and :Gsplit, :Gvsplit,:Gtabedit, ...). Edit a file in the index and write to it to stage the changes. Use :Gdiff to bring up the staged version of the file side by side with the working tree version and use Vim's diff handling capabilities to stage a subset of the file's changes.
Bring up the output of git status with :Gstatus. Press - to add/reset a file's changes, or pto add/reset --patch. And guess what :Gcommit does!
:Gblame brings up an interactive vertical split with git blame output. Press enter on a line to edit the commit where the line changed, or o to open it in a split. When you're done, use :Gedit in the historic buffer to go back to the work tree version.
:Gmove does a git mv on a file and simultaneously renames the buffer. :Gremove does a git rmon a file and simultaneously deletes the buffer.
Use :Ggrep to search the work tree (or any arbitrary commit) with git grep, skipping over that which is not tracked in the repository. :Glog loads all previous revisions of a file into the quickfix list so you can iterate over them and watch the file evolve!
:Gread is a variant of git checkout -- filename that operates on the buffer rather than the filename. This means you can use u to undo it and you never get any warnings about the file changing outside Vim. :Gwrite writes to both the work tree and index versions of a file, making it like git add when called from a work tree file and like git checkout when called from the index or a blob in history.
Use :Gbrowse to open the current file on GitHub, with optional line range (try it in visual mode!). If your current repository isn't on GitHub, git instaweb will be spun up instead.
Add %{fugitive#statusline()} to 'statusline' to get an indicator with the current branch in (surprise!) your statusline.
Last but not least, there's :Git for running any arbitrary command, and Git! to open the output of a command in a temp file.