You should be able to adapt your Contax/Yashica-mount (C/Y-mount) lenses easily to any mirrorless camera system (Micro Four Thirds, Sony E/FE mount, etc.) without introducing any new glass into the system.

Some C/Y lenses can be easily adapted to the Canon EF/EF-S mount line of cameras with a simple non-optical adapter; others would extend too far into the camera body and may interfere with the mirror. That's more of a problem with the full-frame EF-mount cameras, but something to be aware of. There is a compatibility list here. The "1.3" and "1.6" columns in the chart reflect APS-H and APS-C formats, respectively. The "I" in the "5D" column means the lens will interfere with a full-frame mirror. (The "FF" just means the lens offers full-frame coverage. Silly, really, since all of the C/Y-mount cameras were full-frame 35mm.)

Other DSLR mounts would place the lens too far from the sensor to achieve infinity focus without introducing additional optical elements. (Several camera brands have slightly shorter flange register distances, but not shorter enough to allow the adapter to be solid enough for use.) There are optical C/Y-to-whatever adapters made (with varying degrees of quality) by a number of different manufacturers, but that's rather like using a third-party teleconverter with all of your lenses all of the time. The optical quality with remove most of the "star" from the "T-star" lenses. And while those lenses may have been exceptional at the time they were made, the demands of high-resolution digital are somewhat more stringent than all but the highest-resolution films. You don't want to give up any quality at all unless you have to.

There are also companies (including Leitax, mentioned in ruffp's answer) that will do a permanent mount conversion to your weapon of choice. That's not a cheap option, but it can be a reasonable choice if you know you're going to stick to one maker's camera system.