An Intel GPU would fit your constraints, but Intel doesn't produce any discrete hardware, so it's only an option if you're buying a new motherboard or CPU.
Why are you discounting nVidia and ATi hardware? They're basically the only discrete GPU hardware vendors, and you're unlikely to find any hardware cheaper than a low-end ATi GPU (for example, this Radeon 3450 from newegg). It's difficult to find second hand hardware as cheap as that once you include shipping.
All modern ATi and nVidia hardware will drive two displays. The only thing you need to look out for is the type of connectors - if you've got two DVI monitors, you'll need to ensure any card you buy has two digital outputs.
I'd recommend an ATi graphics card - the open source drivers are generally good, and AMD releases the documentation so new cards can be supported reasonably quickly. I bought a Radeon 4350 card for about $30 and it works flawlessly with Ubuntu 10.10, including compiz.
Additionally, if you want to go for more than two monitors, ATi “Eyefinity” cards can support up to 6 monitors - although all but one have to either connect using DisplayPort or use DVI and an active DisplayPort→DVI connector.
The open driver work from the archive (that gets set up by default) generally works on my ATI Fusion-based laptop. It's decently fast but not as fast as fglrx.
The fglrx drivers in the archive were faster, but would freeze my laptop once every few hours. The Catalyst 11.4 drivers that I manually installed from their website are the fastest and I've had no crashes yet.
Some people are reporting that disabling vsync has helped them:
Best Answer
I believe Unity requires 3D graphics. So if there is an open driver that can do that, you don't require proprietary drivers.
Looking a the status of the FLOSS nouveau drivers, currently you probably would need the proprietary drivers for NVIDIA, however, they are working on the necessary features.