I'll add some supporting info here...

The blue-colored cable you have there is the "RGB" and it's capable of passing the lowest resolution signal of the three. Lately I've seen RGB plugs push a full HD signal to a TV or projector, but I'm surprised because that's rare. I also know that some (many?) flat-panel TVs automatically have a limit to what resolution they'll display when you use that port on the TV. I've sometimes seen blurry, smeary colors with this port, especially when using a KVM switch (multiple computers sharing one keyboard/mouse/monitor), so I avoid it.

The cable with all the pins and flat tabs of metal in it is the DVI cable. That will output a really good, clean signal all the way up to 1080p (1920x1080) resolution.

HDMI is also the highest resolution port, like the DVI cable. If you don't have an HDMI out on the machine that's connecting to the TV, then you can still use your TV's HDMI ports by buying a simple HDMI-to-DVI adapter: it has the pins and tabs to plug into that port on your machine on one side, and on the other is a port to stick an HDMI cable into, that you can then plug the other end of the HDMI cable into the TV. I do this on an older laptop and get full 1080p.

Don't get shafted on price with these cables and adapters: I've had good luck going to Newegg or Amazon and buying Rosewill, Mediabridge, or Amazon's new branded cables. You can walk into a store and get charged a lot of money for the same thing if you're not careful.

Hope that helps!