In my humble opinion, nothing beats the classic Europe map, but the variants can be a lot of fun, too. These are my favorites on this site, excluding the classic map, because it's the best, though I know there are probably a thousand that aren't here.

1. Ancient Med - Its opening phase might be the most boring of all time, and the map seems to be split into two parts (Rome/Carthage, Greece/Persia/Egypt), but overall I'd say it's pretty fun, and it's great if you want a quick game with only 5 players. It's probably monotonous for some, but it's my favorite because there are less players to worry about (which might be a drawback for some), and just enjoyable. Plus, it's funny to think about how your Roman army uses tanks.

2. Fall of the American Empire - Way better than the other ten player variant, and less chaotic. It's not exactly balanced (Cuba never does well, it seems), but hardly any Diplomacy map is. It seems very difficult to win, with the number of supply centers needed to win being 34, but overall it's a pretty good map. It usually varies as to who rises to power, with the exception of Peru, who usually seems to be a major player.

3. World Diplomacy - Maybe I like it more than Modern because I used to play Risk, and it's nostalgic for me, but I think this map is fun. It just. Takes. For. Ever. Fun when it finally kicks off, but everything about it just seems so drawn out, and people usually just draw because it takes months. And one or two weak players can concede an entire continent, giving a better one a somewhat-unfair advantage. If it didn't take five years, this one would be more fun.

4. Modern Diplomacy - Why is Bosnia on the map? Poland? Switzerland is a supply center? And Gibraltar? It's just hectic. It's the largest stab-fest out there. That being said, it's decently balanced for having four million centers to put in.

But Classic will always be number one.