Some people recommend watching television to improve your listening in Japanese, but I found I made my biggest gains in 聞き取り (kikitori, listening), 発音 (hatsuon, pronunciation) and リズム (rizumu, rhythm) by listening to 音楽 (ongaku, music).
音楽の好みは個人の自由です (Ongaku no konomi wa kojin no jiyū desu, Music is a matter of personal taste), of course, and the 歌 (uta, songs) you like will differ in テンポ (tenpo, tempo) and 歌い方 (utaikata, style of singing). I prefer ロック (rokku, rock) and パンク (panku, punk) as a matter of taste, but any genre will do as long as it has clear 歌詞 (kashi, lyrics).
歌詞 are the key. I'm used to buying CDs and I have a ton of them by Japanese bands. CDs will almost always include a 歌詞カード (kashi kādo, CD jacket with lyrics) that you can use to memorize the songs and sing along with them. I prefer to write out the 歌詞 into a notebook along with 振り仮名 (furigana, the small hiragana written above kanji) so I would know the correct 読み方 (yomikata, way to read) and 言い方 (iikata, way to say) for the words. Copying them out also helps with memorization.