For me, no one above peak human in strength, agility and durability can qualify. And Captain America I wouldn't consider a vigilante; he's a leader for other superheroes. Black Panther is a monarch in his country, so he's out.
Here's mine, in alphabetical order:
Batman
Daredevil
Moon Knight
Nightwing
Punisher
Captain America spends no time going out on a nightly patrol to catch thieves and rapists. His concerns are bigger; threats to the country, the world, some of which are cosmic. Avenger business is full time for him. Batman is a leader in the JLA, but that's only in his spare time; his primary business is crime in Gotham City.
It would have to be:
1. Batman. Kind of an obvious choice. He's just generally awesome, in mainly every aspect. Call me fanboy all you want, but I reckon he's the coolest vigilante out there. Great martial artists, great gadgets, great intelligence. Coolness in a can.
2. Daredevil. As most people's second on the listers go, mine is DD. An original power that is really cool and can be put into use in some many great ways. Plus, a scary rogues gallery, and some great reads in comic wise. A good fighter too, which I seem to like in my favourite characters.
3. Deadpool. Funny, funny, funny, funny, and funny. And damn cool. Did I mention funny?
4. Punisher. A bad ass as far as they go. The toughest, most hard as nails character in comics, IMO. It's amazing how skilled that gun-toting street leveler is. Seriously cool. Good fighter, and packing a whole liad of powerful weaponry. And he managed to win the Mr T award by scaring people by driving a van.
5. Hmmm... I don't know. Probably either Black Panther or Moon Knight... it's a tie. They both borderline just about on street level vigilantes anyway.
Isn't Spider-Man sanctioned by the Avengers which works in unison with the United Nations? I don't think he's considered a true vigilante anymore.
The Avengers lost their U.N. sanctioning in Avengers Disassembled. So, they still have ties with S.H.I.E.L.D. and the U.S. government, since they operate on American soil, but nothing so broad as it once was.