I use the .LOG datestamp behavior in notepad on Windows frequently, but my editor of choice is vim or gvim, so I wanted to emulate notepad's behavoir more precisely than the solution suggested by unSpawn.
Although modifying .vimrc (or _vimrc on Windows) was fairly new to me, I used unSpawn's approach as a starting point (writing an InsertDate function) and combined it with an autocmd which looks for the .LOG at the beginning of any file:
execute "normal O" . strftime("%Y-%m-%d %H:%M") . " \<Esc>"
autocmd BufReadPost * if getline(1) =~? '^\.LOG$' | call InsertDate() | endif
As you can see, I prefer the ISO8601 date format standard, but you are welcome to use whatever date format you prefer. I hope others find this useful.