Sounds like Japanese beetles. They are horrendous! Try Bayer or Sevin to get rid of them. They love roses, clematis, basically, everything! Sorry I don't have a pic, but just type Japanese beetles on the Internet and I'm sure you'll find a pic.

I looked up pictures and descriptions of Japanese Beetles, and I don't think that is it. They say JB are 3/8 inches long at mature size. These are much larger, and look somewhat different too. I have not seen them on plants, just slowly crawling om the ground. I grossed myself out by reading some posts here about JB. Especially the one about the bug in the ear. I realized then that these can not be JB's, as that would be physically impossible with these monsters. What else could it be?

I don't know what they would be, but if they're not harming the plants, I wouldn't worry. They'll go thru their cycle and die. Unless they are harming your plants or they swarm so bad they get all over you, I wouldn't bother with chemicals. You could be doing more harm that way to beneficial insects.
Let us know if you find out what they are.

Kat

Any chance they are cicada bugs? If so, I don't think they are harmful. We have them in our yard right now.
Rachel

No, these are not cicada-bugs either. They are wing-less critters, large and somewhat slow moving. The most upsetting thing about them is their numbers and SIZE. Killing them is not easy either. They have a hard shell and seem to be able to take a lot of pounding. When I succeed in killing one it leaves quite a mess behind, and simply is unpleasant (and gross...) Does anyone know where I might be able to bring one in to be identified here in the Chicago area?)
Thanks everyone for trying to help.

Elisabeth, here's a link to the U of I Extension Service offices. They would be able to ID the insect and tell you how to deal with it.

V.

Here is a link that might be useful: U of I extension service

Or you can search the site and/or contact the people at www.whatsthatbug.com.

They're very nice and will reply to you relatively quickly with an answer if they can provide it. If you can send them a digital picture, that will help.

I've used them a couple of times since moving here and they were wonderful.

Here is a link that might be useful: What's That Bug?

We're over run with Cicadas right now - They've been metamorphosing out of the larva state. I've been watching them emerge on nights that I've been up late - I've grown a little attached to them!

If this is what you have (either the emerging insect or the larval part), don't worry about your garden, they're harmless (but a bit noisy).