Here's my list:
Estonia and Finland (technically not bordering though)
Latvia, Lithuania and Estonia (I'm thinking of the Baltic way)
Belarus and Russia (well, I don't think any other former Soviet state has better relations with Russia)
Serbia and Montenegro (although they split in 2006)
Romania and Moldova (although I might be wrong here)
Turkey and Azerbaidzjan
India and Nepal (not sure?)
Laos and Vietnam (although I've also read that some people resent domination by Vietnamese, just as in Cambodia)
Peru and Bolivia (although it seems some people in Bolivia expect Peru to give them some of their coast because Chile ran off with it...)
Germany and Austria (not sure?)
Albania and Kosovo (that is if you recognize Kosovo)
Bulgaria and Macedonia (probably somewhat ambiguous)
Armenia and Russia (not really bordering though...)
also: the Benelux: Belgium, the Netherlands and Luxemburg. Especially the Flemish region( where I live) has all in all good relations with the Netherlands. The Flemish government and the Dutch government have set up the Dutch language union to work together to regulate the Dutch language, an international organization which is pretty much unique in this aspect.