I'm planning to write a web service to automate some task for my Outlook.com email account. I want Outlook.com to send an HTTP request to my endpoint when an email arrives, so that I don't need to poll the server. Does Outlook.com provide such functionality?
Outlook provides webhooks via what they call push notifications. You'll find details on this API in the Outlook Push Notifications REST API reference. The capability exists to receive events for a wide variety of resources, including email messages in Outlook.com.
You might also find some useful capabilities for notification of changes to messages with Use the Microsoft Graph API to get change notifications and Keeping messages and mail folders up to date in apps.