Try the Wikipedia article on DisplayPort.
DisplayPort has active and passive adapters. From the
users point of view, one big difference is price.
Things like VGA, you suspect that can't be passive,
as VGA is analog and DisplayPort is digital. So that
one is going to be more expensive and an "active" converter.
DisplayPort to HDMI should be passive. At least, as
long as the DisplayPort has an HDMI mode.
http://en.wikipedia.org/wiki/Displayport
"However, Dual-Mode DisplayPorts are designed to transmit a
single-link DVI or HDMI 1.2/1.4 protocol across the interface through
the use of an external passive adapter that selects the desired signal
and converts the electrical signaling from LVDS to TMDS."
So you're looking for video cards with a "Dual-Mode DisplayPort".
Or, if the video card is lame, a capable active converter.
http://www.newegg.com/Product/Product.aspx?Item=N82E16815158351
"Unlike a passive adapter, the MDP2HDS actively converts single-mode and
dual-mode DisplayPort output, which is ideal for graphics cards that do
not output dual mode/multi-mode (DP++) signals, such as ATI Eyefinity cards.
The Mini DP to HDMI adapter is compatible with Intel Thunderbolt , when
connected directly to a supporting DisplayPort over Thunderbolt I/O port."
"Maximum Digital Resolutions: 1920x1200"
So it's not the perfect adapter, because it doesn't do the
higher resolutions.
Now, when I see an "active" device, I look for a power source.
No power adapter comes with that thing, which means there must be a power
pin on DisplayPort connectors. From the Wikipedia article...
Pin 20 DP_PWR Power for connector (3.3 V 500 mA)
So there is a source of power to run the active adapter,
and no wall wart is needed (apparently). If the converter
needed more power than that, then you'd need an adapter.
Chips are available that easily run off 3.3V now. Chip designs
can go as low as around 1.0V or so, but then it becomes
difficult to do higher amplitude I/O signals with such a
low source. With 3.3V, that can do lots of I/O standards
in an adequate way.
Paul