'Ne' is one of ending particles that add various emotions to the statement. The primary function of '....ne.' is to seek an agreement and/or confirmation from listener. 'Ne' invites the listener's cooperation and engagement into the conversation by agreeing the statement.
If the intonation is up at the end ('.....ne?'), the sentence becomes literal tag question, which is expected to be agreed.
You can use 'ne' both in polite speech and casual speech.
(example)
"Kono neko, kawaii desu ne!" :polite
"Kono neko, kawaii ne!" :casual
(Both means "This cat is cute, isn't it!")
However, over-use of 'ne' should be avoided. As it creates agreeing atmosphere, too much 'ne' may sound too intimate and too pushy. Then, how much is too much? Probably it will be safe to use it only in situations where you'd use tag question if in English.
Also, 'ne' is only used in conversation. Never in formal writing.
As other answers indicate, 'ne' sometimes sounds feminine because it makes the statement rather softer than simple declaration.
Especially, '...wa ne.' '.....no ne.' are used only by female. But I think 'ne' as an agreement seeking mark is no problem for men to use. (Men who want to show off their masculinity would avoid 'ne'.)