A certain kind of lens (called "Petzval Lenses") are very much in vogue because of the swirly effects they produce. You'll have to make up your mind what you think, but when used tastefully and subtly I rather like the effect .
Here's a Flickr gallery I made of some images with the Petzval swirl, and a few that claimed to have swirl but which are definitely not the real thing: http://www.flickr.com/photos/richard314159/galleries/72157624453174055/.
Does your camera swirl?
Obviously the first thing is to try it and see. You may be surprised. I was when I took a Tokina wide angle lens out a few months ago. This was a lens I had had for years and years, quite liked, but thought I knew it very well, what it could and couldn't do. But I just took some close-up shots of blossom and didn't think anything of it until I had scanned the negatives. I didn't see anything special in the (TTL) viewfinder when I took the shot, but to my astonishment when I looked at the scans, I got lots of swirl:
You need to know what sort of conditions to try, to get the swirlies. When your eye is "in" it gets a bit easier, but to start with make it easy for yourself. You need to focus on something close - so twist the focus right out and get in close to something interesting. You need to have lots of interesting background all out of focus. And you want that background to have lots of tiny points of bright light. Go into the woods on a sunny day, take someone to photograph, or photograph the leaves and branches but always keep an eye on the background for the light coming in between the leaves. To make the background really out of focus open the lens right out to its fastest aperture.
Home-made swirly lenses
So maybe your lens doesn't swirl. You may have noticed that the best swirlies come from very big large format cameras with these old Petzval lenses. (This is, I think true.) What do you do? Buy such a camera and lens?
Well maybe. But it will cost you a lot, and not just money: these cameras are expensive and complicated to use, and the really good swirly lenses are pricey too, and you must have the right lens for the right camera. (With a swirly lens on a camera that's too small you just don't see the swirl.) All this means there's a lot to learn.
Lot of people say Petzval swirl is impossible on small cameras such as 35mm SLRs and DSLRs. I beg to differ. I have done it. But it is harder.
Why does it swirl?
The popular opinion is that a lens fault called astigmatism causes swirls. This may be true. Petzval lenses do have astigmatism. In fact it is certainly true, to some extent: astigmatism does make a lens swirl under certain conditions, but it is not the only reason, and possibly not the main reason.
My theory is that, in most cases, the lens swirls because it has the shape of a long barrel and the swirls are caused by the circular aperture at one end mismatching the circular aperture at the other end. Petzval lenses always had a slot for an aperture in the middle to avoid this problem. (And it's only the crazy people that want the swirls that leave this out.) Other effects like spherical aberration and astigmatism then might help more and make the swirls more pronnounced or change them slightly.
This means to make a lens that swirls you need to make it in a long barrel. Also make the barrel just the right length and the diameter just right too.
The geometry of a long barrel can be simulated by a long tube with two apertures at each end. I made apertures by cutting black card into circles and cutting holes in them. (Be careful: they have to be exactly circular and central.) Otherwise the lens is just like the one I talked about before on this blog. You just need two (roughly equal) close-up filters at the ends of the tube, with an aperture on each.
Here are some examples.
They all work. But it is not easy to get these lenses right. As I said, the holes at each end have to be just the right size. Too small and you only see a circular image, too big and you miss the swirls. The focal length of the glass and the length of the tube is important too. Keep experimenting and you'll get there.
This was done with a home-made lens on a 35mm SLR. I got my 4/3 DSLR to swirl too.