Many years ago, while fishing the Green Drake on Penn's Creek in PA (the one and only time I've done that) and the legendary crowds were almost as thick as the bugs, I caught a guy from Willow Grove (near Philly) with my back cast on a #10 Green Drake Wulff dry. He was a nice one, in full Orvis plumage, close to 90 kg., I'd say. But he didn't fight anywhere near as well as what you'd think he would for his size...
I've caught most of the fish Jonathon listed on his opening post, with the exception of the Rio Grande whatsits. I've caught a lot of fallfish on the fly at home in PA. They are pretty ubiquitous all through the coolwater/warmwater streams of the Susquehanna watershed. Got a couple nice ones over the years, 18" or so.
I've caught quite a few walleye on the fly, although nothing of any real size (all under 20"). Almost all my walleye came while fishing for smallmouth in streams in PA's Allegheny basin when they were somewhat off-color. Where walleye are present in these streams, these cloudy water conditions seem to make them move up into a lot of the holding lies that the bass normally use. The back sides of in-stream boulders and 2-3 foot deep pockets, etc.. No muskies on the fly. I may set my mind to this once we move back to NW PA. There are a lot of them around.
I've caught lots of steelhead (Lake Erie variety), a few Lake Trout (many years ago in Algonquin Park just after ice-out), a small bull trout (12" or so..) out of the lower Deschutes. A few small west slope cutts out of some small McKenzie tribs in Oregon. In 35 years of tromping small PA trout streams, I got one wild tiger trout, about 6.5" out of a trib of the Loyalsock. Only wild tiger I've ever seen, let alone caught
In terms of oddities, I caught a gar that went about 22" (I don't know what kind) out of Presque Isle Bay on Lake Erie, white and yellow bass out of Kincaid Lake in southern Illinois (white bass not such an oddity, yellow more unusual), a yellow bullhead out of the Manitowoc River while fishing for bass, something called a Bigmouth Buffalofish out of the Big Muddy River, again in way southern Illinois, fresh water drum (sheephead) out of the Illinois Fox River and Lake Erie and a Hellbender (accidentally) out of French Creek in NW PA.