Vintage suits, if done right, can make you look either hip, or tacky, depending on the way you go.
The definition can mean different things to different men. It really depends on your sense of style and, usually, your age. However, here are some types that are generally considered to be "vintage".
Mod - These designs were extremely popular during the 60s. You probably remember them being worn by the Beatles on their television appearances. With the right kind of guy, this look can be pulled off. 60s nostalgia seems to be in a little bit, and it can work if you have a little bit of a hipsterish vibe.
Miami Vice - The epitome of 1980s fashion for men. I loved this show!
Leisure - These say 1970s all the way. These are probably best used at a costume or Halloween party.
Disco - Yes, we all remember Saturday Night Fever. That movie put these into popular culture. However, best used in a costume setting for sure, unless you are actually going to a disco.
Pimp - It's not really PC but they can be fun in a costume or Halloween party.
Zoot - These were very popular in the 1940s, but would be tough to pull off today. Even in a club the baggy look isn't where it is right now. Unless you are Jim Carrey in the Mask probably best to stay away.
1920s - The 20s had some interesting fashion, and for being over 80 years ago, still has some popular elements. Ascots are still popular, and a dapper suit from the depression era could look cool in the right setting.
1950s - The 50s were a little more conservative and had less of a flair. Most business wear was pretty straightforward.
1960s - In addition to the mod look, the emergence of Mad Men has made 60s style business wear popular. The Don Draper look can definitely catch a look of a lady who likes that classic look.
Sharkskin - Another product of the 60s, these high class suits haven't enjoyed as much of a renaissance as the other styles. These were often associated with the "Rat Pack" in Hollywood, especially the grey variety. Calvin Klein still makes a couple designs of these.