As an addition to Habi's answer, if you want to do it without using taglist, you can quite easily define a function that will work it out. It depends what language you're programming in, but for C-like languages, you can do this:
nmap ,f call ShowFuncName()
" Show the name of the current function (designed for C/C++, Perl, Java etc)
fun! ShowFuncName()
let lnum = line(".")
let col = col(".")
echohl ModeMsg
echo getline(search("^[^ \t#/]\\{2}.*[^:]\s*$", 'bW'))
echohl None
call search("\\%" . lnum . "l" . "\\%" . col . "c")
endfun
Put that it in your vimrc and then press ,f to see the current function.
Taken from here.