Buying a car with the bike rack in mind I am in the process of buying a new car and I want to fit a rack on it for my bikes. Are there any issues that I need to be aware of for fitting a rack to a car, or rather are their any factors that would make it impossible to fit a rack to a car? That would be a deal breaker for me.
Sharing own experience with several racks, either used as bought and even homemade.

I can divide them in three categories:

Roof
Trailer Hitch
Trunk/Reardoor.

Roof:

More adequate for small cars (i.e. not so tall) for reach issues. Also, they work better with lighter bikes (Road bikes, XC bikes or the like). I wouldn't fit a heavy DH bike in a roof rack, it's heavy to lift up to the roof. Also if the car is too tall, the operation is likely to get difficult. In My experience, the roof rack would work fine if the car's roof is at your shoulder's height, above that, it gets too difficult.

There are two kinds: the ones that hold the whole bike or the ones that hold the bike by its fork. Either one has the advantage of easily accepting odd shaped bikes, as they usually have a rail in which the rear wheel fits. 

If the whole bike type, they have a rail for the front wheel and a post that holds the bike upright. When sturdy enough they can handle heavy bikes like the DH ones. 

The fork type requires you to remove the front wheel completely and put the fork in a hitch that has the same shape and dimensions as your wheel's axle. This of course works better if you have a quick release front axle, and along having to take your bike apart every time, you risk loosing axle nuts or springs. Also, you need the rack to have the adecuate hitch for your bike's front axle: road and XC hubs are different, All Mountain or DH bikes usually have thru axle type. However, they hold the bike very secure. 

A useful advantage of the roof rack is that it is unobtrusive for most doors, so you have full access to your car without having to remove bikes. Also, they can be left on vehicle as it doesn't increase overall length, so is not a problem for tight parking and other slow maneuver. (Unless under a low garage or bridge).

Other advantage is that they usually can accommodate more bikes than other types. For example, I used to fit 3 XC bikes on top of a small car without protruding outside the roof. Another example: the support cars in Tour d France...

Trailer Hitch:

Better for bigger cars that are more likely to have adequate mounting points for the towing bar (what the hitch is bolted to), as this is the only mounting point unlike other rack types that have several mounting points.

This type is more likely to hold the bike by it's tires and have a post that holds the bike upright, so you don't have to disassemble the bike anytime just to transport it.

They are usually limited to three or four bikes.

Consider that they increase overall car length but can be left on vehicle. Also, in order to be sturdy enough they usually are heavy therefore difficult to install/remove by just one person. If they are too low they can hit the ground in certain situations. In some cars it will block the rear door, even when the bikes are not in the rack. Some can be folded up to be left in the vehicle when not in use.

These are very goo options for DH or AM bikes that use to be heavy, because this kind of rack does not require you to lift the bike too high. They are also useful for oddly shaped bikes, as most DH or XC frames can be.

Trunk/Reardoor:

Therese light racks are easy to install/remove by one person, and are specially adequate for lighter bikes. Every maker of these will claim they are universally compatible with any car, however, this is not true, some are better for sedans, some for hatchbacks. For sedans they can interfere or damage a spoiler. For Hatchbacks they can interfere with rear window wiper.

This rack type is better suited for straight top tube bikes and  they can be hardly fitted with some full suspension bikes or any other bike that doesn't have a diamond shaped frame (there are temporary addaptors that are fitted between the seatpost and the stem post for this purpose.).
They also grab the bike by its frame, so they can damage paint and can also be an issue for carbon frames.

They are usually limited to two or three bikes, and they better be light ones. Some people mount them in the hood too. (it funny to see a car with two bikes attached a each end)

They don't add too much to the overall length of the vehicle and can be left on when not in use. Most designs allow access to the trunk/rear door when bikes are not on them.

If they fit too low can let bike hit the ground in certain circumstances.

There are a variety that fits attached to the rear mounted spare wheel, these are not compatible with harcovers for the spare.

Other Options: 

Other options you may consider are pickup trucks which exist in many different sizes and you may find one that fit all your needs (besides bike transport) They offer huge flexibility and carry capacity. Personally this happens to be my most recent circumstance (did not acquire the pickup because of the bikes) but is also the most comfortable one. I can carry from just one bike up to seven plus driver, riders and gear (my pickup is medium sized, not one of the biggest).

Another option can be a small trailer for bike carrying. This can be fitted to almost any vehicle, as a bike towing trailer will not bear too much weight. However it may need to be custom made /installed and it is more complicated to drive a car with a trailer attached. Nonetheless, a custom made bike carrying trailer, if well designed, can be very comfortable to use.

Finally: Consider the type of bike you are going to carry, and your other needs (Me for example, use the car for bike carrying just 2 days a week). Ease of use of course will make your biking journeys more enjoyable, so, congratulations for considering it! ;)