Modern graphics cards have three outputs:
DVI-I means "DVI-Integrated"; this connection contains the outputs for both VGA and DVI-D. So if wish to use a monitor's DVI input you simply use the normal DVI cable which will only hook up to the DVI wires. For VGA, you use a VGA "adapter" which works by connecting only to those wires meant for VGA.
DVI should always be used instead of VGA if possible.
A VGA output on a graphics card is ONLY compatible with a VGA input on a monitor.
I don't believe HDMI outputs contain any VGA connections. You can use HDMI to hook up to a DVI or HDMI input. You need either an HDMI->DVI adapter PLUS the DVI->DVI cable, or else simply an HDMI->DVI cable.
1) HDMI is capable of carrying both video and sound. If you hook up to a DVI input you lose the sound portion as DVI carries only video.
2) Graphics cards can only output specific audio, such as the audio format for movies such as Dolby Digital (AC3) and others. It's basically useless because it can't pass Windows sounds or Video game sounds, only movie audio so I can't understand why anyone would use this. It also does not pass through more advanced audio sounds. *The graphics card has a dedicated onboard audio decoder which decodes only specific sounds.
3) Many newer graphics cards can output HDMI out of the DVI connector. The HDMI output wires have been included along with the VGA and DVI wires. You need to use the graphics cards included DVI->HDMI adapter for this to work (a normal DVI->HDMI won't hook up to these HDMI audio pins).
4) HDCP means "High Definition Content Protection"; to play BluRay content on your PC, both the graphics cards DVI or HDMI output must be HDCP compatible, as well as your PC monitor. All HDTV's are HDCP compatible.
Example of BluRay PC setup:
1) DVI->DVI (monitor DVI is HDCP compatible)
2) BluRay Reader (SATA)
3) any sound card/chip and desktop speakers
4) BluRay compatible software (Nero and a few others)
1) VGA monitor inputs can use a VGA output or DVI output with DVI->VGA adapter
2) HDMI without audio is the same as DVI
3) BluRay requires HDCP on both ends
4) audio output from graphics cards is almost useless
5) People with large video collections wishing to hook up to a PC should use either the Western Digital TV LIVE HUB, or a Boxee Box. The WD 2TB Elements drive is a great addition to either. The WDTVLIVEHUB has an internal hard drive (930GB usable). Some people may prefer the Boxee Box interface. There are Pros and Cons to either.