Pick a pair of quiet, low-saturation colors that are
similar in value, but not identical. (In other words, one
needs to be a wee bit darker than the other.) Good choices
are blue and white, beige and white, or two similar shades
of gray -- assuming the text on top of them is dark, anyway.
Generally, one of the colors is your page's background color.
Alternate the color from row to row. If the rows are thin, you
could also experiment with grouping the rows: the first
three are white, the next three are blue, etc.
This pattern virtually eliminates the need for horizontal
lines between the rows (though you could use lines, if they
are very thin and inconspicuous). If your columns are aligned
with each other, you don't need vertical lines or a heavy border
around the table -- the viewer's sense of visual closure kicks in,
and the row colors define the edges of the table for you.