Yes, you can share your games with your family. Steam recently introduced Family Sharing, a system where a user can share his library with the rest of the family and others who use the same computer.
You simply need to enable Family Sharing on the computer you want to use:
- Log in with the account you want to play with
- Log in with the account that owns the game
- Go to settings > Family > Authorize This Computer...
- Authorize the borrowing account by checking the box under Authorized Accounts
Note that two users still cannot play the same copy at the same time.
Also note that not all games support this system, or have only partial support. For example, you cannot participate in CS:GO's competitive matchmaking while borrowing the game from another account. Most games with 3rd party DRM, such as Uplay, will cause issues and might not even show up on the list.