Can you sell T-shirts with photos YOU took of other things?

Specifically cars. Can you take a picture of a car and put it on a T-shirt and sell it? Even with the cars emblem and name showing? For instance, if the "ford" badge was clearly showing would you still be allowed to sell it? And if not, would you be allowed to crop the badge out and sell it then?

Yes you can, however if they are special cars such as at a car show or race cars, you should have permission from the owner.

By default the author of any art work, including photos, own allrights to his/her work. Most objects are fair game to shoot and use the images commercially or any way you want. If an object was created by someone and has special value as an art or design piece (including a custom car) it might be necessary to get permission from the author of the art/design object to publish it commercially. Photos used commercially of people require the model's permission usually obtained as a model release. Failure to do could could result in a an invasion of privacy law suit by the model.

No
This isn't a matter of copyright law, but of trade marks.

There are some pretty weird trademarks out there, such as the coke bottle, Mickey Mouse's ears, or the shape of particular guitars.

About the only real exception to this is parody, with the rule of thumb being you need to change about thirty percent of a logo to use it. So for instance, taking a picture of a broken down Ford, with the caption "Fix Or Repair Daily" would be legal, but just having a humpfist picture of a Mercedes grill with logo would not be, because Mercedes want to sell such humpfist pictures themselves.