No, you can remove Outlook Express (it's in the Windows Components section of Add/Remove Programs) without issue, or just ignore it. Don't just delete folders however. That's generally just a bad idea.
I use Verizon FIOS Webmail which does all I want it to do. I am wondering if I need Outlook Express for any reason. If I right click on a document in My Documents and click on "E-mail this file" I get an Outlook Express (OE)window. When trying to Send the message with attachment I get a window saying the Server is my old earthlink address which I left a year ago and I can't send the message. I cannot find OE on Add or Remove Programs list of Currently installed programs and updates. A search shows multiple files and folders that have Outlook Express in them. Will deleting these have bad consequences?