Yes. Other examples: I appreciate you/her/him/them. I appreciate my math teacher. I appreciate my math teacher for his patience. I appreciate my math teacher’s patience.

I agree with all of these comments and i would only add that “i appreciate you” typically suggests a deeper level of regard or affection. It is not just the activity that you appreciate but rather the person themselves. Perhaps it is similar to estar and ser in that “i appreciate you” is more about the persons characteristics and “i appreciate your help” is about something like a transient experience or state. Hope thats helpful.

The short answer is, it's a casual, informal way of saying "thank you," but it's not strictly grammatically correct. The more correct form would be "I appreciate your help," "I appreciate the work you did," etc., as in your example. The long answer: It's a little complicated, because there are circumstances when you *can* talk about appreciating a person. It's just that the meaning is somewhat different. The Oxford English Dictionary gives several definitions for the word "appreciate," and the relevant one for your question is this: "to be grateful for or appreciative of (kindness, a favour, etc.)" The examples that the OED gives are sentences like "I appreciate your kindness," "I'd appreciate any information you can give," "I appreciate your suggestions," etc. But there's also another definition which is very similar: "to recognize as valuable or excellent; to find worth or excellence in; to esteem." This definition *can* be used with a person as the object. "These citizens don't appreciate a good king." "After getting to know him, I learned to appreciate him better." So it's not necessarily wrong to say that you "appreciate someone." Strictly speaking, though, the meaning should be that you regard them highly -- not that you're grateful to them. That said, many people do use "I appreciate you" as a causal way of saying "thank you." So while it's not exactly "correct," it has become a fairly normal usage.

It's more deeply personal to say, "I appreciate you " It means they appreciate your being, rather than just your help. I wouldn't say that to anyone unless I was in a very close relationship with them.

I would say it is an informal usage but one that is creeping into the lexicon rapidly; one appreciates the attributes/actions/etc. of a person, not the person directly.