Initiating a game on Steam will annoyingly pause all of your active downloads but at least there's been the option to alt-tab your way back and manually resume downloading. It's a workaround that shouldn't need to exist, and Valve is finally making progress here.
A recent Steam client beta update adds the option to let games download while a game is running. There's only one small problem: the feature is on a per-game setting. So it's still not as seamless a process as it could be. The update also includes improvements to the user interface, Big Picture mode, and the Steam client for Linux -- find the list below or at that link.
- Add ability to limit what time of day Steam is allowed to automatically update apps
- Add option to let other games download while a game is running (this is a per-game setting)
- Add download regions for Calgary, Edmonton, Winnipeg, and Ottawa in Canada
- Add 'Copy all text to clipboard' context menu option in the System Information dialog.
Steam client UI
- Improve downloading status text at the bottom of the main window
- Added ability to opt into game betas and edit launch options
- Added Inbox item under Linux if your machine requires a reboot due to OS level updates
- Fix infinite loop of Cloud sync error dialogs on game launch
- Fixed mouse cursor being visible during startup animation even if it hadn't moved
- Fix paste pasting stale text.
- Fix Ctrl+C/Ctrl+V in client-hosted web page text controls.
- Fix incorrect foregrounding of a blank window in some -silent startup cases.