A Shimano Nexus 8-speed hub will work on a vertical dropout bike. Its not as simple as saying, 'its the same as a single speed hub'. Various components of the hub need to 'indexed' or 'aligned' to properly function. Verticlal dropouts vs. horizontal vs. reverse dropouts all poistion the mechanisms in a different orientation.
To account for these differences Shimano provides a variety of 'ant-turn' washers, which in turn properly orient the hub various mechanisms.
Refer to this link: http://bike.shimano.com/media/techdo...9830600211.pdf
for installation instruction including washer descriptions.
With vertical dropouts, as d2create mentioned, you'll either need:
1. That magical tooth combination or
2. A chain tensioner.
That being said, I have 4-speed Nexus 'freewheel' setup and cant say enough about it.
1984 Schwinn Paramount; 1987 Schwinn Paramount; 1975 Tom Ritchey, 198X Vitus