Make Money
The best thing to do with a rock is to sell it for money. While common rocks will only provide your Sim with a few Simoleons, rare rocks such as the Pink Diamond can be worth thousands. To sell a rock, click on it to put it in your inventory and then enter your inventory screen to sell it directly. Select the rocks you wish to sell and drag them to the Simoloens symbol at the bottom of the inventory screen.
Improve their Worth
The value of any rock in the game can increase if you have it cut or appraised. Only gem stones like emeralds and rubies can be cut by a jeweler. To have a stone cut, click on your mailbox to send it out. Space rocks can be appraised at the Landgrab Science Facility in town. Open the town map, click on the Landgrab Science Facility and select "Appraise Space Rock." Both of these features cost money, however the value of your rock will increase when you sell it, offsetting the cost.
Decoration
All rocks that your Sims collect can be put on display in and around their homes. With the rock in your Sim's inventory, enter "Build and Buy" mode and select "Family Inventory." Select the rock and place it wherever you like, either on the ground or on a surface like a table or counter. Send your gems to be cut by the jeweler to change their look so that they better suit your Sim's home.
Completing Challenges
Collecting rocks is necessary to complete a number of character challenges. Collect 16 different space rocks to complete the "Amateur Rock Finder" challenge, which makes it easier to find the rest of the rocks. Collect all 10 gem types to complete the "Gem" challenge and unlock the "Heart Shaped" cut for gems. Collect one of every space rock and gem in the game to complete the "Awesomest Rock Collector in the Universe" challenge, which makes rare rocks appear more often.