Opt+arrow cursor manipulation stopped working
Solution 1:
I found the answer.
Even though it wasn't selected, I did have installed "Unicode Hex Input" as an Input Soure (along side U.S) in the Keyboard->Input Sources preference pane. I removed the Unicode option altogether, and the opt-arrow shortcut started working again instantly.
Solution 2:
This helped me find the solution for OS X 10.6/Snow Leopard, which is a little different. The Input Sources tab is under System Preferences->Language & Text, instead of Keyboard. I had Unicode Hex Input installed and enabled; unchecking it fixed the Option-Arrow problem, and re-checking it again doesn't seem to bring the problem back! Very strange. I'll probably leave it unchecked just in case.
Edit: More details. It looks like the actual problem has to do with the Keyboard & Character Viewer item in the menu bar. (This appears as a national flag when nation-specific input is selected, or a yellow-on-purple "U+" when Unicode Hex Input is selected.) When Unicode Hex Input is selected in the Keyboard & Character Viewer, the Option-Arrow keys don't work in some apps. You can leave Unicode installed and enabled in Language & Text->Input Sources, but it can't be selected in the Keyboard & Character Viewer.