One of the best things about Fujifilm cameras is the built-in film simulation modes, which give you various monochrome options, Astia, Velvia, Provia, and more. I find that they aren't too harsh, and seems to mostly improve the look of my photos. They aren't applied to the RAW file, so it doesn't take anything away from the image.
However, there's also an "Advanced Filter" mode, which gives you some more filters and effects. Although they are a lot more obtrusive. There's quite a few, including partial colour filters, soft focus, and pop colour. But the one I have the most fun with is "Toy Camera". The description it gives is "Create shaded borders as taken by toycameras. (nostalgic effect)".
I can't say it will produce the most professional photos, but as a person that enjoys retro camera apps on the iPhone, such as Dispo, Huji, and Hipstamatic, it's fun to have it directly in my real camera too.
Here are a few quick examples:
I'll have to give the other filters a try now, and I'll see what I can get when I can actually leave my house and go somewhere interesting.