The first thing to understand here is that じゃん forms a tag question, so it's entirely different than the negative form:
このゲームは楽しい。 This game is fun.
このゲームは楽しいじゃん。 This game is fun, isn't it?
このゲームは楽しくない。 This game isn't fun.
このゲームは楽しくないじゃん。 This game isn't fun, is it?
じゃん is an informal version of じゃない; this use of じゃない as a tag question was covered by Tsuyoshi Ito previously.
Since 形容詞 (けいようし; "い-adjectives") have different conjugation patterns than 形容動詞 (けいようどうし; "な-adjectives"), you can easily tell when a tag question is being used. But you know that with 形容動詞, じゃない may be present in the negative form. Without additional context, the following could be ambiguous:
便利じゃない。 It's not convenient. Or, It's convenient, isn't it?
In this example, intonation distinguishes tag questions from negatives: a tag question will put a rising intonation on じゃない, while a negative will put a falling intonation on じゃない. (じゃん, however, is always a tag question and never forms a negative.)
In writing, this ambiguity can be cleared up by using a question mark or the question particle か:
便利じゃない？ It's convenient, isn't it?
便利じゃないか。 It's convenient, isn't it?
Additionally, it's worthwhile to discuss here the difference between じゃない (じゃん) as a tag question and the sentence-ending particle ね:
あの映画、けっこうおもしろかったね。 That movie was pretty good, wasn't it?
あの映画、けっこうおもしろかったじゃん。 That movie was pretty good, wasn't it?
With ね, the speaker is merely making a statement and anticipating the listener will agree, but じゃん can often imply that the speaker wants to convince the listener to agree. In the above example, you would use the first sentence after seeing a movie with a friend without any prior expectation of how good the movie would be. But the second is more appropriate if, for example, your friend went into the movie thinking it would be bad, and after seeing it, you wanted to get him to agree with you that it was in fact a good movie.