After buying an AmazonBasics HDMI cable I noticed a "HIGH SPEED with Ethernet" sticker in the connectors. I didn't know what it meant so I searched a bit to find out what these cables are capable of. I hope this article makes clear whether you need an HDMI with Ethernet cable or not, and how to make use of the Ethernet feature.
If all you want is the good ol' HDMI cable, it doesn't matter whether it has Ethernet or not. All HDMI cables work for the vast mayority of applications, which are normally just transferring HD video and audio. Any device needing an HDMI cable can use an HDMI with Ethernet cable just fine.
HDMI with Ethernet cables are meant to provide Ethernet connection (Internet and local network access) to devices that support Ethernet over HDMI. For example, your computer may be used to provide Internet connection to your TV without an additional cable or WiFi, which is slower. The devices at both ends must be HDMI Ethernet Channel capable in order to have a connection. If at least one of them is not, the cable will work just as a standard HDMI cable.
HDMI with Ethernet speed
The HDMI with Ethernet cable is capable of delivering 100Mbit/s speed, the same speed of Fast Ethernet, but slower than Gigabit Ethernet, which is only achievable throught a separate Ethernet cable. 100Mbit/s is however, more than enough for today's needs taking into account that the HDMI cable is itself used for video so the Ethernet connection is unlikely to be used for streaming high quality video.
Devices that use HDMI with Ethernet
According to hdmi.org:
[Ethernet over HDMI] accommodates current and future IP-based networking solutions for consumer electronics, including DLNA, IPTV, LiquidHD, and UPnP.
In January 2014, after Googling for a couple of minutes I couldn't find of a specific device that supports Ethernet over HDMI. Until device support is introduced, this feature will remain unused. It's going to be several years before Ethernet over HDMI is widely supported. Remember HDMI with Ethernet capable devices are needed on both sides for the connection to work. Next generations of TVs, consoles and Blu-Ray players will have to add support for us to take advantage of this feature that removes yet one more cable from the back of our TVs.
High Speed vs Standard HDMI cables
A far more important decision than whether to buy cables with Ethernet support is whether to buy them Standard or High-Speed. There are four types of HDMI cables for home use: Standard, Standard with Ethernet, High-Speed and High-Speed with Ethernet. Standard speed HDMI cables are rated up to 1080i. High-speed HDMI cables are rated well above 1080p, which is the maximum possible resolution from today's game consoles. Standard cables might well support resolutions above 1080i, however buying High Speed cables is recommended for 1080p and 4K support. Buy high speed cables to future-proof your purchase and be sure they'll work. The price difference is generally small.