Why countries join the "Coalition" in Iraq

In A Call to Arms Kristof talks to foreign members of the "coalition". An Estonian woman sites the following reason for going to Iraq:

It is in our interest to be friendly to the U.S.," she said, "because we are hoping that the U.S. and NATO will protect us if Russia attacks."

Kristof also speaks to foreign leaders (PM of Estonia, Pres of Ukraine) and concludes:

And that's the problem with our coalition: it's mostly made up of leaders counting on rewards, rather than of nations that are really behind us. Tony Blair genuinely believes in the Iraq war as a matter of principle, but the other members of the coalition are mostly opportunists trying to buy good will in the Bush administration.

Sounds about right to me.