According to HDMI.org any current and future cables with number naming conventions such as HDMI 1.3 and HDMI 1.4 is not being compliant. HDMI 1.4 can only be used to refer to the HDMI port and not the cable itself.
But refering to HDMI cables here is the run down:
HDMI 1.3:
Only can support stereoscopic 3D and side by side 3D effectively... and it may not be in 1080p (may not have the bandwidth to support 3D 1080p). It supports resolutions up to 1080p (1920 x 1080)... but for 3D video it will not be in 1080. These ususally produce 3D effect like a card board cut out (at least from my experience). Some HDMI 1.3 does not have the Audio Return Channel.
High Speed HDMI (or HDMI 1.4)
Supports Audio Return Channel
There is alot out there that supports up to 1440p = 3D in 720P but still not 1080p... for 3D it is two pictures created for a 3D effect so 1440p divided by 2 is 720p. You have two pictures at 720p to create the 3D effect.
For true 3D 1080 you need a High Speed HDMI cable that supports 2160p (4k x 2k)... 2160p divided by 2 is 1080p...you will also need a cable that supports a refresh rate of at least 120Hz (60Hz x 2 = 120Hz for 3D)... For a cable that does do 2160p, 10.2Gbps, and at least 120Hz refresh rate and is licensed/certified by HDMI and is HDMI compliant do not usually run cheap.
High Speed HDMI with Ethernet:
Does everything as a regular High Speed HDMI mentioned above - but the main difference is that it has a 10/100 ethernet channel for data transfering. Currently there are no HDMI devices that support the 10/100 ethernet in these HDMI cables - but they may have it in the future so it may be a good idea to future proof your cable purchases with these types of HDMI cables. The 10/100 Ethernet may come into play if Internet TV becomes popular.
More explaination here for HDMI 1.4:
http://www.hdmi.org/manufacturer/hdmi_1_4/index.aspx
Here are the differences of HDMI cables:
http://www.hdmi.org/manufacturer/hdmi_1_4/finding_right_cable.aspx
Cable Gauge also comes into play depending on the length of the HDMI cable you need... the longer the cable the lower the guage you need = more copper in the cables need to effectively transfer the HD video and HD sound.
Some standard HDMI cables such as HDMI 1.1 and 1.2 may only display up to 1080i and not 1080p... some of them do not support HD Audio Bitstreaming. Only HDMI 1.3 versions and higher support HD Audio Bitstreaming...(also explains why some cheap HDMI cables you cannot get sound when connected to a digital audio receiver).
If you have time here is wikipedia for HDMI:
http://en.wikipedia.org/wiki/HDMI
All this does matter sometimes in the price you pay for cables!