It was a T.V. series, not a classic one, a mix between paranormal stuff investigation and comedy. I remember the generic, the music was entertaining. I think there have not been many episodes but I'm not sure.
It was aired in the 80's.
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This definitely sounds like it's describing Mork & Mindy.
Whilst premiering in the 1970s, this continued into the 1980s, and had 94 episodes, which could be seen as not many if compared to, say, Doctor Who, which has over 800 episodes according to Wikipedia (can't post link due to low rep).
I doubt anyone could argue that this doesn't contain comedy, and in episode 6 of season 1, a reporter offers a reward for proof of alien life, and Mork hands himself in (http://www.imdb.com/title/tt0651214/), which is what made me think this fit the bill in terms of paranormal investigation, aside from the obvious fact that Mork is an alien.
I found the music in the theme song to be very entertaining, although I doubt that this would be to everyone's taste.