I've been having the same issue as described and tried many things to no avail. But I believe to have fixed it completely. I changed router from WEP encryption to WPA2, connection has been rock solid (20 mbps up and down) for about an hour now on all my iOS 8 devices that were having issues (iPad 3, iPhone 5, iPhone 6+). I hope this helps some if not all of you experiencing issues.
I use WPA2 already, so I doubt that's it.
I've noticed that the Wifi range I'm getting had dropped dramatically. Looking at my router's diagnostic page, my iPhone's transmit signal strength is much lower than it used to be, which would make it much more susceptible to interference. I'm finding that my iPhone switches to the 2.4 Ghz band much more often than it used to as well.
I used the Wifi Sweetspots app someone posted in this thread and can see the speeds drop to nearly nothing at times when I'm not moving at all. It seems better if I'm right next to my router, but that wasn't necessary before.
I have similar problems with my work place's Wifi. There the Gmail app sometimes tells me I have no network connection and I have to press refresh to get mail to load.
My office's IT department had actually put out a warning against upgrading to iOS 8 saying that doing so would result in the loss of the ability to connect to the corporate Wifi. They put some kind of fix in for that, but it's still officially in testing.