You can steal some very valuable vehicles while playing Saints Row, but by default you don't have permanent ownership over them. This page of the guide explains how to permanently save your vehicles by storing them in your garage.
Garages in the game world
Garages let you permanently save stolen vehicles and take them out whenever you wish. Every saved vehicle remains in your garage permanently, unless you manually delete them.
Your first garage can be found by the heroes' hideout. The initial hideout is your apartment, the garage door being located by one of the building's walls. Later in the campaign you'll relocate to an abandoned church. You can then access the garage by interacting with the open space by the building.
You can also make use of JimRob's Garage. This is an early-game venture you can use to make profits.
To save a vehicle there you must drive into the building. Striking a deal with JimRob's Garage unlocks vehicle tuning as well. We've described it in more detail on a separate page Vehicle tuning - how to unlock?.
All garages share the same vehicle list. There's never a need to visit one specific garage - any one will do.
Saving a vehicle in a garage
To save a stolen vehicle you must drive it to one of your garages. Remember you can only interact with garages if out of combat and not being chased by the police.
You can visit the garages to view the list of owned vehicles at any time. You can also tune them and take them out with you. Delivering a car already saved in your list will number the subsequent models. All saved vehicles are available in infinite quantity. You can take them out of the garage as many times as you'd like, even if you end up destroying them. The only way to permanently remove a car from the garage is to manually delete it from the list.
The vehicles acquired by completing missions and optional activities will be saved in your garage automatically. You don't need to take them there to save them.