Can I connect a DisplayPort monitor to the Thunderbolt port on a Mac, and vice-versa?

Connect a DisplayPort display to Thunderbolt port

As Apple says on their Thunderbolt product page:

And because Thunderbolt is based on DisplayPort technology, the video standard for high-resolution displays, any Mini DisplayPort display plugs right into the Thunderbolt port. To connect a DisplayPort, DVI, HDMI, or VGA display, just use an existing adapter.

To confirm this, here's what Intel says:

And Thunderbolt enabled products are compatible with existing DisplayPort devices so you don’t have to go buy a new display to take advantage of a Thunderbolt technology enabled computer.

_{... emphasis mine.}

This means that you can attach your DisplayPort-equipped monitor to any Mac with a Thunderbolt plug. If your display has DisplayPort only (i.e. not Mini DisplayPort), you will of course need an adapter to do this.

For the other display, just use the HDMI connection. You could also daisy-chain two displays together, if these displays support it and have two DisplayPorts each.

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Connect a Thunderbolt display to (Mini) DisplayPort

The opposite seems to be possible, as the physical connection is the same. However, Apple states differently. Their tech specs don't mention the Mac Pro being capable of using it. The problem will be that you can't update the display's firmware and use the data pipe.

So, all in all, it won't work.

Ars Technica has a recent article about this, which states that there might be issues:

What is really going to rub folks the wrong way, we suspect, is that the Thunderbolt Display is not configured to work with a miniDP display plugged in to its Thunderbolt port. It wouldn't be surprising if more than one user with an existing 27" Cinema Display or other miniDP display got a Thunderbolt-equipped Mac and ordered a Thunderbolt display expecting to be able to add the miniDP display at the end of the chain.

Apple's just released a support document about their Thunderbolt-based displays here: http://support.apple.com/kb/HT4885

Note this bit:

Mini DisplayPort displays will not light up if connected to the Thunderbolt port on an Apple Thunderbolt Display (27-inch).

So there will be no daisy-chaining MDP and TB-based displays from the looks of it.