Is there an official Unity web badge (which would point to the Unity web player download page) that I can place on web sites that use the Unity web player?
As the new guy here at OTEE I’ve recently wondered the same thing. I don’t believe there is an official download badge nor any guidelines for how to instruct the user to install the player. This is something I’ll be discussing with others in the office so we can decide on official artwork and how to present that to the user. In the meantime you might follow the Unity Web Player download page model: Unity Real-Time Development Platform | 3D, 2D, VR & AR Engine
When we have something “official” we’ll make sure to have it visible on the site and make a post here on the forums.
On the same note a official and slick prerendered animation with the unity logo would be great for opening credits.
Bill
I’ve thought of that as well, we’ll see how it pans out. 
Prerendered would be a bad idea - huge downloads. An nVidia-like realtime animation would be great though.
i’ll agree with the above!
Obviously any such animation would need to be (a) small in file size, and (b) entirely optional to use. But let’s start a different thread on this topic if it’s of interest, I don’t want into animation chatter buried under a heading about install badges.
It would be great if there was a version like the “Made with Macromedia” graphic, with a transparent bg to put on a web page.