This page explains a very small collection of the many reasons to believe in a young earth (thousands not millions of years) as described by the genealogy of Israel's royal family starting with Adam as recorded in the Bible.

The Earth's gravity is decreasing year by year and would be too great to support life than modern science says existed many millions of years ago.

The Earth's path around the sun is a squashed spiral, not an ellipse--millions of years ago the earth would have been too far from the sun to support the life that modern science says existed at that time.

When we landed on the moon (even if you believe the first time was a conspiracy, we've been there several times now!), we used dust-proof equipment and expected to land on millions of years of loose dust, which would add up to several feet--instead, there was only less than ten thousand years worth of dust, only a few inches. The idea that the moon appeared on the scene at that time does not match our knowledge of buildup of space dust, formation of celestial bodies, or the orbit of the moon. And, without the moon, the earth would not have enough warmth at night (among other things) to support life that modern science says existed at that time.


Despite the fact that starlight takes a great amount of time to reach earth, starlight could easily be set in place by an being that is infinite in power, precision of using his power, and independent of our four dimensions. A night sky over earth that lacked starlight (or stars that completely lack the slight variances in hue we observe) would be boring, don't you think?


Sources:
answersingenesis.org
drdino.com disclaimer: you may disagree with Kent Hovind's view in his past legal dispute, but this (ad-hominem) doesn't hinder some of his journalism from being useful.