I'm looking actually for something similar to Deft, only for Vim. Does anyone know of any with which he/she has had good experiences?
Check out vim-notes: https://github.com/xolox/vim-notes
It's a fairly sophisticated, and yet simple, note-taking platform. It doesn't have Deft's incremental search etc (I've used Emacs, so I know the features), but therefore you can tag your notes very comfortably, use auto-complete and, of course, search through the files. (The search is Python-based and so somewhat faster than vim-grep).
Just like in Deft, your notes are stored in one folder.
BTW, I think I found it while struggling with the exact same question as yours -- having recently moved to Vim, I needed an alternative to Deft.
UPDATE: Also, you could check out the CtrlP plugin: https://github.com/kien/ctrlp.vim. An excellent tool that allows you to search file names incrementally. It's very fast, nicely customizable and pure vimscript (so no external dependencies are needed).
There are other scripts on vim.org but these ones are the closest, I think.