Project ideas:
I asked on a Linux tech forum for Linux professionals for project ideas that reflect what Linux folks do in the "real world," and these are some of the project ideas they submitted:
Turn a Linux server into a router and firewall.
Set up a documentation server using Apache and a wiki of choice.
Set up a multi-boot system with different types of file systems, including files/directories shared by all users and all operating systems (include Windows and two different Linux OS distros).
Set up some form of groupware on Linux, and configure for access by several users.
Install a demo or OS version of a system administration program; there are several available for Linux that provide an advanced central GUI-based resource for most administration tasks.
Set up a Samba server for print, fax and home directories to be used by both Linux and Windows systems.
Install and test a variety of applications written for Windows onto a Linux machine.
Get a Linux server and a Windows server to communicate and share resources, while still maintaining appropriate security.
Set up a Linux box as a webmail and mailing list server.
Set up a Samba server for print, fax, and home directories to be used by both Linux and Windows clients.
Set up a DNS/DHCP server to be used by both Linux and Windows clients.
Install and configure a Linux-based software program to perform a specific task. The Linux-related magazines (online and paper) are a good source for ideas in their ads. Many products have demo or free versions - find out the specifics before committing!
A project focused on virtualization that includes Linux and other open source software
A project focused on security that includes Linux
A project focused on embedded Linux (you'd have to supply your own devices)
Something that combines any of these things
Something else that you find that sparks your interest
I'll add others as I can!