If possible it is recommended to avoid converters where possible, however here is a guide to possible conversions and what type of adaptor that is required to minimise problems. An adaptor probably exists for all conversions.
VGA is an analogue signal, to convert between analogue and digital signals an active adaptor is required.
There are two types of DVI signalling standard; DVI-A (analogue) and DVI-D (digital). These two standards are combined in the DVI-I connector which is able to process both types of signals by having pins from both available in it's male and female connectors. It is most common for sources to have a DVI-I female connector and to change the cable with the male connector where relevant.
Along with the two signalling standards, there are also two standards for different resolutions that a DVI connector can support. These are single and dual link video. Single link DVI will support up to 1920x1200 @ 60Hz resolutions, whereas Dual link DVI will support up to 2560x1600 @ 60 Hz resolutions. A Dual link DVI connector can support single link resolutions but not vice versa.
HDMI shares the same video signalling standard as DVI-D however it also has embedded audio. Most converters will strip the embedded audio from the HDMI signalling standard.
DP / Mini DP / Thunderbolt all share the same signalling standard and can be converted with passive cables as it is only the connector that differs. A DP++ port is required for passive conversion from DP to HDMI or DVI-D, and this passive adaption will only support single link resolutions.
|DP++||single link DVI-D||✓||✘|
|DP++||dual link DVI-D||✘||✓|