Hosting Center

Database-as-a-Service

alwaysdata
Windows Azure
cloudControl offers a fully managed platform-as-a-service solution with MongoDB as one of their powerful add-ons. Read the blog post MongoDB Setup at cloudControl for more information.
dotCloud
Heroku has add-on connectors to allow you to use from MongoDB from Heroku applications
RedHat OpenShift
VMware CloudFoundry

MongoDB runs well on both virtualized and non-virtualized servers.

(mt) Media Temple's (ve) server platform is an excellent choice for easy MongoDB deployment.
A2 Hosting has a quick installer to add MongoDB to your VPS hosting account. Instructions for running the installer are on A2's wiki
Dreamhost offers instant configuration and deployment of MongoDB
LOCUM Hosting House is a project-oriented shared hosting and VDS. MongoDB is available for all customers as a part of their subscription plan.