OP,
Is your HDTV CRT, LCD, or DLP technology? Assuming it's NOT CRT (which tends no to have this problem, if I remember correctly):
Unless your TV has a "Game Mode," you're probably going to have a problem. Your PS2 is outputting a signal at 480i (maybe a few titles do 480p?), and your HDTV has a fixed pixel display of either 720p or 1080p (vertically aligned pixels). The problem comes from the fact that your TV has to scale the image, which necessarily takes time. Only a few ms, but enough to make games like Guitar Hero very difficult to play.
Most modern consoles have the option to scale the signal to whatever the resolution of your TV (except the Wii). This cuts down on the problem considerably.
If your HDTV is older, you're stuck unless you purchase a current-generation console (which you should, because they're awesome). Older (especially DLP) HDTVs had crippling lag. Newer HDTVs are much better about this.
Xbox 360 FTW!