A file with the .CDR file extension is most likely a CorelDRAW Image file, which is a vector image created by CorelDRAW to hold text, images, effects, shapes, etc., usually for the purpose of creating letters, envelopes, web pages, banners, and other documents. Other CDR files might be Macintosh DVD/CD Master files that hold folders and files in a single archive for the purpose of burning data to a disc, much like the ISO format you might be familiar within Windows. The Raw Audio CD Data format uses the .CDR file extension too. These are ripped/copied music files taken from a CD. Yet another use for CDR files is as Crash Data Retrieval Data files. These are generated from sensors installed in vehicles that are using a Crash Data Retrieval (CDR) device.
Since there are multiple file formats that utilize the .CDR file extension, you have to first understand which format your file is in before you can know which program can open it.
If you know your CDR file is an image of some sort, chances are it's a CorelDRAW Image file. The same is true for the other three; if you're on a Mac, consider your file a DVD/CD Master file, or a Raw Audio CD Data file if you suspect that it's music. Files taken from a Crash Data Retrieval device are in that format.
Open CorelDRAW Image CDR Files:
CDR is the main file format used with CorelDRAW software. They can be saved as templates if the same document layout needs to be used again, which is where the CDT format comes from. They may also be compressed and saved as CDX files.