If you are running VGA, you will need to set the size in the TV most times(most have an auto set option).
With HDMI you may have overscan or underscan. This has always need even on all sides however. So if you had black all around the screen, you would need to adjust the overscan options in the TV menu or video card. The same would be said it everything was running over the edges of the screen leading to part or all of the taskbar being cut off.
Overscan has nothing to do with cheap or not cheap tv's and has everything to do with how the TV boardcast network was set up way back when. It is a form of backwards compatibility because older boardcasts used to have noise and even closed caption information on the edges of the image. TV's cut this off so users never had to see it. The amount of overscan varied from screen to screen.
With TV's and computers using the same interface you may have these kinds of issues.
As the user above mentions, video cards control panels will allow some correction of these issues.