HDMI is only a "standard", it is not the "best" connection available. DVI is generally superior and our preferred connection to a computer monitor.
With the increased amount of output ports on today's graphics cards it is not unusual for the HDMI port to have limited space for connection. Oversized HDMI cables may not fit correctly. (see picture below)
Above is a picture of the common outputs on the GTX 970 graphics card.
Top row from Left to right - Dual Link DVI - HDMI - Display Port (single link DVI port just below the Dual Link DVI port)
HDMI (v1.4) is digital and has a standard resolution of 1920 x 1080 with an Audio signal (also supports up to 4096×2160 at 24 Hz or 3840×2160 at 30hz)
HDMI 2.0 increases the maximum TMDS per channel throughput to 6 Gbit/s. This enables HDMI 2.0 to carry 4K resolution at 60 FPS.
DVI (Dual Link) is digital and has a maximum resolution of 2560 x 1600 with the Audio signal being optional. Single link DVI has a maximum resolution of 1920 x 1080.
Display Port v1.3 is digital and has a resolution of 3840 x 2160.
Display Port v1.4 is digital and supports a resolution of 3840 x 2160 and up to 7680×4320.
The old VGA (Dsub) is an analog connection.
If your graphics card does not have a HDMI connector as above and you want to connect it to a TV then a DVI to HDMI cable (or convertor) will be required as below.
If you are trying to connect multiple HDMI monitors to a graphics card as below then you will need a DVI to HDMI cable as above.
To connect 3 monitors to the above would require 1 x HDMI cable and 2 x DVI cables (or DVI to HDMI Cables)