The most common one I can think of -- and it's been a problem for me twice this week alone -- is IE6 and the box model bug. Look it up!
Specifically, the problem I'm thinking of is when you have floated DIVs which the developer thinks all fit within a wrapper DIV, but they don't in IE6 because they're slightly bigger.
So rather than three columns, you end up with two, and your third is down at the bottom of the screen somewhere -- you want:
+-------------------------------+
|+------+ +-----------+ +------+|
|| | | | | ||
|| foo | | bar | | baz ||
|| | | | | ||
|| | | | | ||
|+------+ +-----------+ +------+|
+-------------------------------+
but you get:
+-------------------------------+
|+--------+ +------------+ |
|| | | | |
|| foo | | bar | |
|| | | | |
|| | | | |
|+--------+ +------------+ |
|+------+ |
|| | |
|| | |
|| baz | |
|| | |
|| | |
|+------+ |
+-------------------------------+