This is something I've always wanted in Outlook. You can 'Categorize' emails and assign a color, but this does not change the color in the Outlook Inbox view.
The work around for me was to create a 'Custom Flag' with a 'Due Date' in the past. This will turn the text of the email in the Inbox view to Red.
You can also set up some Advance Formatting Rules to change the Font(color, size, underline, bold) based on the Category, but this takes some time. Here is the link for that: http://www.howto-outlook.com/howto/coloremailadvanced.htm
Here is a sample of what it looks like: