Use YouCompleteMe for code completion in Vim
When I first started using Vim, code completion was one of the two things that I thought was missing that almost made me switch back to a full blown IDE like Eclipse, but thank god I stuck with it and didn't switch back (the other thing I thought was missing was the ability to ctrl + click on a function to find it's declaration).
Fear not citizens, enter YouCompleteMe: finally a good, intelligent code completion plugin for Vim. It's free, fast and will save you lots of time. Couple YouCompleteMe with Supertab and you'll be even more of a coding machine than you already are in Vim.
Alternatively, if you're a python developer only, there's also a plugin called jedi-vim which uses the awesome Jedi for code completion which is pretty similar and also pretty gravy.