What type of cables are you using to connect the television?
You should seek to use cabling in the following order of quality:
1. HDMI
2. DVI or VGA
3. Component video or coaxial from a digital source.
4. S-Video
5. Composite video
6. Coaxial from an analog source.
If you're relying on 4, 5 or 6 it's no wonder you're seeing interference. Avoid them if at all possible, even for standard definition applications. A high def television will show the inadequacies of a low quality connection even more clearly than a standard TV. For playing video games you should at the very least be able to employ a component video connection. If you experience interference with that or better then there is something wrong.
For your cable connection, you can try to set up digital reception of as many channels as possible if your TV has a digital cable ready (QAM) tuner. Alternatively you can request high definition service from your cable company. It may cost a bit more, but they'll likely provide a high-def box with quality connection ports along with the service upgrade.