This page explains why, sadly, a TV will never look as good as a monitor, when hooked up to a computer.
Long story short, lots of legacy TV and broadcasting baggage means a "television", even with a nice, perfect, digital HDMI connection, won't ever be sharp.
UPDATE, December 2020: IGNORE MY OLD COMMENT ABOVE. (Unless you're trying to connect an old computer to an old TV.) A lot has changed in 8 years. This actually works now. TVs no longer run at the odd resolution of 1366x768. Most are one of the two actual HD resolutions: 1280x720 or 1920x1080. These can be run just fine via HDMI. You can even run a 4k display as long as you have good enough cables. You might still need to check for overscan settings.
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