I also had issues with drag and drop in OS X Lion. Although I could drag and drop within the same application, I had a lot of issues dragging and dropping into other applications. Most of the time, I would drag, switch applications (using Cmd-Tab), and find that (1) the icon of the item I was dragging would get stuck in mid-air (even if I was no longer holding down the trackpad "button"), and (2) I could actually interact with the window I was trying to drag to, e.g., I could actually type in Mail.app even though I was still holding down the trackpad button.
I did not have anything such as AirParrot, iDisplay, etc. installed, and I had no rogue kernel extensions that I could pinpoint as the cause.
In my case, it was apparently a bad com.apple.ink.framework.plist file. However, I was able to fix drag-and-drop by doing the following:
1. I first removed com.apple.ink.* from my ~/Library/Preferences folder, logged in/out, and let OS X generate a clean set of files.
2. When I logged back in, an Ink window showed up in the bottom right corner. I clicked the left-most button (the one that looks like a pen), which switched it to a mouse cursor and which I believe turns off sketching, clicked >> and went into Ink Preferences, then flipped "Handwriting Recognition" on and off a few times.
3. After logging in and out again for safe measure, drag-and-drop finally started working.
Back when I was running Snow Leopard, I had plugged in my friend's Wacom tablet for a few minutes to play with it. In the subsequent process of installing/uninstalling software for this tablet, something modified my com.apple.ink.framework.plist file in a way that later messed with drag-and-drop when I upgraded to OS X Lion.
This is probably not a permanent fix for those of you who actually use Wacom tablets, but I thought I'd share my solution with those who still have problems with drag-and-drop in the hopes that it will help you.
Additional details
I kept an old copy of my com.apple.ink.framework.plist file, converted both the new (where drag-and-drop works) and old (where it didn't) ones to ASCII text (using plutil -convert xml1) and diff'ed them against one another. The differences are:
The new file contains:
<key>inkMasterSwitchOn</key>
<false/>
which is not in the old file.
The new file contains:
<key>inkWindowVisible</key>
<true/>
whereas it was set to <false/> in the old file.
The new file contains:
<key>recognitionEnabled</key>
<false/>
whereas it was set to <true/> in the old file.
The inkServerPSN also changed numbers.