After installing Unity4 and running it, the license activation window opens and after about 5 seconds small error dialog pops up, pressing Ok closes Unity.
Been trying for about an hour now.
Edit; Looking at process monitor Unity is receiving data from mailsrv02.unity3d.com, reconnect and after 2 seconds disconnects all ports and error dialog pops up. Happens every time.
Can’t say if the server is at fail but want to cover another aspect which I hit:
Ensure that your firewall isn’t blocking it, not even a moment.
I had similar problems on a late beta through Little Snitch on OSX before giving Unity open internet access, as even the time required to confirm the access grant on the dialog was too long. Its possible that this by now has been enhanced and is no longer a problem but thought mentioning it can’t cause any damage
The bug here is that you should be offered to use the manual activation flow which is also prompted by disconnecting the internet and launching Unity.
As Dreamora points out, it could be a firewall issue.
Please try the manual activation flow to activate Unity.
Though this is one-year old thread, thisb just happened to me.
The problem was that I mapped ssl.google-analytics.com to localhost.
Commenting it out worked for me.
Aha! Thanks. That’s what it was for me, too. (Great, do I have to allow google to spy on me at all times in order to use Unity? 
I guess this is what happens when IT people try to write code. 
) Update: No, it starts ok after I uncommented that so that it’s active in my hosts file again. Phew. Presumably it will still check once in a while.
Had the same problem today with launching Unity3D through a proxy.
Adding a user environment variable solved it.
Variable: HTTPS_proxy
Value: Your Proxy Value