Body
GOOD RULE OF THUMB: It is generally preferable to utilize a connection that employs a passive adapter, when possible. Signal is converted less, thus preserving quality.
Definitions
Active adapter - uses the connector's power to run a device (typically a dongle) that physically changes the signal type to be compatible.
Passive adapter - usually a pin-to-pin conversion without additional processing. Much cheaper.
Note: USB-C connectors listed here assume that you are using a USB-C with DP Alt Mode OR Thunderbolt compatible port.
Compatibility
HDMI:
To DisplayPort - Active adapter required. Passive cable will NOT work.
To DVI - Passive adapter or combination cable (HDMI on one end, DVI on the other) will work. Audio will NOT be carried.
To VGA - Active scaler required. Active adapter typically won't deliver good results. This connection is not recommended.
To USB-C - Active adapter required.
DisplayPort:
To HDMI - Passive cable (DP to HDMI) will work.
To DVI - Passive cable (DP to DVI) will work.
To VGA - Active adapter required. Some signal degradation will occur. Generally not recommended.
To USB-C - Passive cable (DP to USB-C) will work.
DVI:
To HDMI - Passive adapter or combination cable (DVI to HDMI) will work, but audio will NOT be carried.
To DisplayPort - Active adapter required. Passive cable will NOT work.
To VGA - DVI-I or DVI-A connectors can use a passive adapter. DVI-D connector requires an active adapter.
To USB-C - Active adapter required.
VGA:
To HDMI - Active scaler required. Active adapter typically won't deliver good results.
To DisplayPort - Active adapter required.
To DVI - DVI-I or DVI-A connectors can use a passive adapter. DVI-D connector requires an active adapter.
To USB-C - Active adapter required, if they exist.
USB-C:
To HDMI - Active adapter required.
To DisplayPort - Passive cable (USB-C to DP) will work.
To DVI - Active adapter required.
To VGA - Active adapter required, if they exist. Not recommended.