I think this is a great question/topic. The first way I think about approaching an answer is to define "care". If your idea of feeling cared for is getting a hug and being told so, then I suppose that's a pretty easy criteria to fulfill.

For me, I think there's many different kinds of care - like love, it's a big word and it encompasses a lot. There's family love, friendly love, romantic love, even loving an inanimate object (like loving sunsets or the ocean). Care is the same way to me. There's different levels/types of care.

A hug and a kind word is a low-level of care to me. A higher level of care from a therapist might be if I told them I was feeling bad because I love music, and I want to play guitar, but I couldn't find a guitar for $75 or less (my budget), then I come back next week and the T has four printed ads from craigslist with guitars for $75 or less. That's an entirely different level of care. They had to work a little to help me on that one - they worked harder than a hug and word.

To answer your question, no, I have never felt cared for by a T. I keep hoping I will find one that does, but so far, no luck. But I'm harder to please than most (no I don't need a guitar, I already got two thanks). The closest I have felt to being genuinely cared for by a T is when I had an MD tell me that there were a lot of bad therapists out there, in addition to the good ones. I liked that guy. He told me that without insurance, I was going to have a much harder time finding a good therapist, because the good ones want to make money, and many of the ones that are paid by social services or government agencies are burned out, overloaded, or just plain low-quality. His honesty and pragmatism impressed me. He didn't care about me, per say, nor did he tell me anything I didn't already know, but he was honest. And being honest like that - well, that to me approaches "caring" in some tangential/abstract way. Cheers.