Could you make something of the correct shape out of either hardware cloth - or, perhaps better, to limit rusting, plastic mesh - lined with fiberglass window screening? If you made a bowl shape, fitted in a frame from which it could be removed for cleaning, then I would think that would serve. It would still let pollen and other fine particles through, but I am not sure anything would screen them out, at least not without a much finer mesh/filter than you could easily find and make yourself.

Pantyhose and a rubber band maybe... You'd have to leave like.. a whole leg on the gutter spout so it doesn't clog the spout. And you'd have to empty it maybe after each rain but if you can get it firmly attached with one of those nice fat bands it would be a very cheap way to implement a filter.

Of course, I haven't done that myself however but seems like it might work lol.

My barrels have a screw-on top lid, so I can lay a contoured cut piece of fine fibeglass mesh under it and screw it back on tight. Works great. But if you don't have that kind of top, you can still get the mesh at HD/Lowes fairly cheap and cut it with scissors to any shape. It comes on rolls at HD and you cut off as much as you need.

Fashioning a frame out of wood probably wouldn't be tight enough to keep skeeters and debris out, but the industrial-sized rubber band post above or really anything that will pull the mesh tight to the barrel top and seal it would probably work if you have something to hold the band on the top side of the barrel.

I cut an entry hole in my rain barrel just barely large enough for a large PVC connector (big on one end, smaller on the other) to fit into. I then put a piece of wire mesh (the kind used for screened in porches and the like) over the PVC connector and secured it with a large hose clamp. I then positioned my downspout over this screened opening.

All large debris gets filtered out and 99% of the water goes in. It works very well.

P.S. This is exactly what I'm talking about above. See Figure H specifically:

http://www.hgtv.com/hgtv/gardening/article/0,,HGTV_3546_2165903,00.html

Here is a link that might be useful: HGTV Rainbarrel How-To