If you like shows that blend all kinds of genres almost seamlessly, you will love Cowboy Bebop. It blends almost every genre you could think of into its story. I wouldn't have been surprised if there was a musical episode somewhere along the way (unfortunately there wasn't :P)
If you like shows with loveable, fascinating characters, you will love Cowboy Bebop. The secretive badass Spike, the blunt but kind-hearted Jet, beautiful and insecure Faye, the strange and oddly flexible Ed and adorable 'data-dog' Ein all team up to scour the universe for bounties to collect. They all have such subtle development over their mostly episodic adventures that your barely even realise how much you're connecting with them on an emotional level until the final episode.
If you like shows that have amazing music to enhance basically everything, you will love Cowboy Bebop. Much like the storyline itself, the music branches across all kinds of genres, but manages to fit their respective scenes perfectly. The final scene and the song that goes with it will stick with me for a very long time.
If you like shows in general, you will love Cowboy Bebop.
It doesn't even matter if you're an anime fan, or you've never watched anime in your life- Cowboy Bebop should be made required viewing for everyone.