Add a table where you have one record for each user. Then add a "join" table to link a given User record to different Projects records:
Users::UserID = User_Projects::UserID
Projects::ProjectID = User_Projects::ProjectID
A portal to user_projects on a Users layout will list all projects assigned to that user. (Fields from Projects may be added to the portal row to fill in additional info such as the name of the project.) Users can use the portal to select projects for their list and you can set up record level access control in Manage | Security to keep users from seeing these lists for other users should that be necessary.