Earlier this year, Star Alliance business class opened way up to Europe, with a veritable bonanza of saver award seats available over the summer from multiple US gateways. Within a couple months, availability had dried back up, which is a reminder to always get in while the gettin's good. The good news is that it looks like the availability tides have come back in for next spring, as long as you're flying from O'hare. I was helping my parents research vacation options tonight, and I found a number of routes with great availability. All the below searches are for two seats, by the way. For instance, here's Chicago to Zurich on Swiss:
And here's Chicago to Copenhagen or Stockholm on SAS:
(There's some journey control going on here, so if you search ORD-ARN, you'll see one-stop availability via CPH, and if you search ORD-CPH, you'll see one-stop availability via ARN. The image above is specifically for ORD-ARN, but ORD-CPH was almost exactly the same. Either way, if you're booking one-way tickets, you can throw away the second segment and effectively fly non-stop to either city.)
Finally, here's Chicago to Warsaw on LOT:
Pretty good, right? Unfortunately, because United's domestic availability is so bad, you may have a hard time finding awards via Chicago from your home city -- even mixed cabin awards. But, if you don't mind starting your trip with a cheap flight on Spirit (in a Big Front Seat, of course) to get to ORD, this could end up being pretty useful.