What kind of HDMI cable should I buy?

There are some hdmi cables called "standard" or category 1 and some called "high speed" or category 2. Standard only go up to 1080i. So it's possible that's what you have. I think it's more likely a player settings problem (or the content it's playing is not "full hd" and its not upconverting it).

More details on cable type: http://en.wikipedia.org/wiki/Hdmi#Cables

Hdmi cables don't need to be expensive, as David said. You can get decent prices at monoprice.com, amazon, ebay, etc. Monoprice used to label their cables standard or high speed so you knew what you were getting (hopefully they've stopped selling the former by now, there really is no need for them anymore). Sellers are not supposed to quote version number, they're just supposed to give a list of the cable's capability. Some, especially on ebay will still say "version 1.4". You likely don't need to worry about it as long as you don't buy a standard/category1 cable (which may actually be hard to find anyway).

A "High Speed HDMI Cable with Ethernet" is pretty much the best you can get right now. Don't worry too much about the ethernet feature, I haven't heard of any devices that use it. As one reviewer once said: "ethernet for all zero of you who need it." :)

its been proven there is no difference in quality on HDMI cables, they all transmit an exact digital signal.

if you aren't getting full HD, thats because the source from watever service you are using on your Google TV is not HD

EDIT: as for people saying "get 1.4" anything you buy on a store shelf will already be 1.4, but the only differences with 1.4 is 4k resolution support (no google TV will support that) and 3D support (which again, no Google TV supports)

Any 1.4 compliant HDMI cable is fine. A $5.00 cable is no better or worse than a $100.00 monster cable.

They're digital cables, they either work or they don't, there's nothing in between.

use the 1.4 type its the most advanced Corvato has no clue what he is talking about