I go to college, and I really like one of my professors. I'm 19 and he is 38. I don't think I would really call this a crush - I just don't know what else to call it. I don't want to have sex with him or even kiss him or anything. I just want to spend a lot of time with him, talk with him, soak up everything he has to say.
I'm not sure what to do about this, either. I haven't acted on it, and don't plan to (though I would really like to). I'm not even sure how I'd go about it, if I was to attempt something. I have no idea why I want this so much. Is this normal? What would you even call it? What do I do about this?

I would call it a crush. And yes it is normal for a student to develop such feelings for their teachers. But it would be very inappropriate for you to pursue it.

It's very normal and not at all unusual, as humans have strong attractions between them regardless of age and good common sense. The challenge is to set your own personal boundaries, and not cross lines of good behavior. That's not easy when crushes and attractions are very intense, its darn hard to even think straight!

You already know you shouldn't act on those feelings, and that's good, just stick with that thought and avoid trouble, complications, and costly distractions, unless of course you don't mind paying the cost of following your feelings instead of your own mind.

LOL, sometimes it's really hard to tell the difference between head, and heart, and in that case do NOTHING, until you can separate the two! The brain wants facts, the heart just wants, and cares little about anything else, so think first, and tell the heart to shut up so you can THINK!

'I just want to spend a lot of time with him..'
Keep in mind that he probably doesn't have 'a lot of time.' You don't even know what his personal life is, I suspect.

There's an old fashioned jokey way of dropping a compliment without being forward or intrusive: Ask him lightly and cheerfully if he has a little brother just like him. That gives him all sorts of options for just laughing at the joke, or answering in a vague way, or answering with any amount of truth and details.
And when he says 'no,' just smile and say 'oh darn' and walk away.

I say all this with the caveat that you should NOT get involved with him, of course. I say it just to help you stop thinking about this so much.
And because it borders on flirting if you linger a second too long, you are asking for trouble.
(You say you don't want any intimacy with him, but I think you are fooling yourself. You take a course from him and that's all the time with him you really need, not with him alone.)

You could also be less coy and more forthright. Tell him that you enjoy his course and wonder if he would have time for a small group of students gathering once a month for discussion.

If that pops the fantasy bubble of being alone with him, then you are definitely fooling yourself, and should just force yourself to drop the whole idea of any of this.