Hi Stephanie -
If the tasks and reminders don't count towards the progress of the project, you could have them create personal tasks in their Work List. Then only they see the task and it doesn't clutter the project schedule.
If the tasks need to track towards the projects progress, they could build a personal project schedule that includes only their tasks and reminders and create predecessor/successor relationships with the larger project schedule so the PM knows the status but it still reduces the size of the project schedule. In doing so, the individual could have work for many projects in one schedule.
Hope this helps,
Teale