There are three main types of bike racks: Strap on Trunk Racks, Trailer Hitch Racks and Roof Racks
Each type has advantages and disadvantages so I'll outline them so you are better informed to make a decision.
Trunk Racks
While these are referred to as Trunk Racks, they will often work on mini vans, SUVs and hatch backs. This type of rack straps to the back of your car with rubber coated metal hooks. Most are very easy to put on and off but this will limit the security if you are going in to eat during a trip. Trunk racks are the least expensive option but are most likely to scuff your cars finish as the rack touches the paint. Trunk racks work well but you have to make sure it is installed correctly or you can have your bikes come off while on the highway. Due to weight limits the maximum number of bikes for trunk racks is often limited to three.
Trailer Hitch Racks
These racks either bolt on to the trailer hitch or go into the square hitch receiver. Because nothing touches the body of the vehicle, they are the safest for the finish. Hitch racks come in two varieties: Fork lift style that holds the bike by the frame or tray style that holds the bike by the wheels like a roof rack. If you have carbon fiber bikes or odd frame shapes, the tray style is the best option as it will take any shape bike without marring the frame. Hitch racks bolt into the receiver hitch so the can be secure. Lock your bikes to the rack and you decrease the chance of your bikes going missing. Hitch racks can hold up to five bikes so are one of the best options for families. The price is higher than trunk racks and you need a hitch but it's usually less money than a roof rack with the same number of bike mounts.
Roof Rack
The roof rack is the most versatile option as you can get more than just bike mounts for it. Bike racks, ski carriers, cargo boxes and canoe mounts are all available so if you are an all round outdoors person this allows you to carry all of your toys. Depending on the the size your vehicle you can mount up to 6 bikes. Roof racks cost more than the other two options as you need the rack and then the individual bike mounts which can add up to over a $1000 for 5 bikes. Depending on the height of your vehicle, it can be awkward to put bikes on the roof. Anything on the roof will usually affect your gas mileage so bear that in mind.
Regardless of the type of trips you want to go on, the best option is the one that keep your bikes safe and doesn't harm your vehicle. Check out your local bike shop to find out the best option for your vehicle.