In Projects, is there a way to see an individual users assigned tasks across multiple projects in a single view? Or do you have to choose each project then view that users tasks?

Yes, it is possible to view the tasks assigned to any particular user across all projects. Click "My Home" option on the top right of the page --> Click "By Users" option shown just below the WELCOME PAGE option --> select the required user from the drop down. Once done the tasks, milestones and meetings assigned  for that particular user across all the projects will be displayed.