Karoo is designed to work with or without a 3G SIM card. However, wireless carriers often require that device manufacturers register their products with them before they allow use of those devices on their networks. This is a long process and Hammerhead is working to get Karoo operational on most large carriers like Verizon(WCDMA Only) etc.
But the following companies allow Karoo to work on their networks. While we do not officially endorse any of them, data-enabled SIM cards from any of them should enable 3G connectivity from your Karoo.
For other cellular carriers, when their SIM is installed you may have to tweak the APN settings that is specific to the country and carrier. We recommend that you use data from the following sites
On the Karoo, go to Settings > Cellular Data > tap + icon on top right, this will bring up a screen like this below, fill in the details from the website above, and then save.