I've seen what you're looking for. On the downspout is a cutout with a screen at an angle in the pipe. The leaves and debris will hit the screen and fall outside the pipe with the water going through the screen, down the pipe and into the cistern.

This Old House had a segment on this a few years ago.

Google "Gutter Drain Filter" and you come up with several designs on the filter. You could probably make one that fits over the barrel top pretty easy. 1/4" x 1/4" galvanized wire mesh and an open cell filter material under that.

Thanks for the replies. Solargary, lots of good info at that link, including the gutter screen that Hendricus described. Dan...well, we don't exactly have a barrel. Here's what we have:
{{gwi:1515324}}From Water

And here's what the tanks look like after sinking them in the ground:
{{gwi:1515325}}From Water

So, you can see that we've got a sizable storage capacity. There will be a pump inside that will send water to our nearby garden, and an overflow pipe that will empty into our small pond. Actually, at our current house we do have 2 rain barrels, and the screening works great. But I think we'll need an alternative sort of Servo-control diverter with this Big Mama system. The ball-valve system looks interesting, although one of the websites, http://ersson.sustainabilitylane.com/rainwatr.htm,
comments that this system is weak in terms of the drainage of the ball-valve limb. However, some of the other plans look doable. So, thanks to all. I would welcome any other comments from others who may have experience with any of these systems.

coffeehaus,

See website below and click on the product selection button. These are specific products manufactured for rainwater harvesting. Vortex filter, smoothing inlet and storage tank floating filter and hose. All are designed to reduce debris from getting into the tanks, to not disturb it once in the tank and to use the most clean water in the tank first.

Hope that helps,

Dan Martyn

Here is a link that might be useful: J R Smith Water Harvesting