Doesn't have to be romance, but they need to be somewhat relevant for each other and interact a lot. My preferences are they're some sort of partners or traveling companion etc. The guy must be a straight serious no-nonsense type and the girl to have a distorted set of values and somewhat a daredevil. I want them to bicker a lot, have clashing opinions and sometimes scold each other (guy scolds the girl more often I guess considering he's the 'sane' one?). I don't need them to be the main characters as long as they have enough part. Can be manga or anime with any genres.

Examples:
Lelouch and CC from Code Geass
Rock and Revy from Black Lagoon
Kyon and Haruhi from Melancholy of Haruhi Suzumiya
Nodame and Chiaki from Nodame Cantabile

Thanks ~

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DONDAKEE!!

aho girl its really an amazing manga but its 4koma though

If you're okay with younger protagonists, try Kodomo no Omocha. And Seishun Away seems headed in that direction.

You could try Nozomi x Kimio, it fits your description.

Crazy For You (Honnosioli)?
Gintama Shinpachi is the straight character usually