How to comfortably interact with famous professors?

From a student's point of view, here is how I tackle the situation. You can break it down by the circumstances in which you meet, and thus guesstimate how much time the professor has for you.

Asking "may I talk to / email you later about...?" can be useful if it's not the right time and place for a useful discussion.

DTK's answer has good points about how you should approach a conversation.

Of course there will be some variations depending on the culture and environment of your department, and how well you know the prof you're talking to.

Hallway / elevator encounters

If they look busy or rushed, perhaps best save it till later. Otherwise, keep questions very brief, concisely answerable, and related to something you know they're interested in (i.e. their own research field).

Discussions at semi-social occasions, such as at a gathering after a seminar, or breaks at a conference

Here, the professor probably has no immediate obligations or things urgently pressing on his or her mind (or else they'd have disappeared by now). This is a better opportunity to ask broader or more complicated questions, or if they work in a related field you could ask for an opinion on a problem you've been thinking about.

Social occasions such as at lunchtime, conference dinner, etc.

As above, but they may even prefer to talk about something other than their own field of expertise -- sports, politics, an interesting paper from a completely unrelated discipline that you read whilst procrastinating, etc. If you don't know the professor very well, you might want to wait for him or her to initiate steering the conversation in that direction.

Find out their other interests (often on book-jackets they authored or on their profile page on the department webpage), engage them in those.

Be respectful of their time. Ask "I heard you are active in topic. Do you have a few minutes to discuss?". If they say no, drop it. If they offer another time, follow their lead.

Do not be obsequious or servile; speak respectfully, but as an adult to an adult. Do not act as a peer, until invited to do so.

Respect the individual and the rank. Keep the values and priorities of the professor in mind. If invited to address the professor by name, do so. If not, address the professor as "Doctor such-and-so" or "Professor such-and-so".

Lastly, always be polite, be kind and listen.

While I am not a "famous professor" I am famous in my field, enough that people routinely want their picture taken with me at conferences. At the same time I get a little starstruck by folks more famous than I am (for example having dinner with the single person who invented the language I'm now considered an expert in, or having him plop himself down next to me while I'm watching a session at a conference.) So I can see both sides of this particular dynamic.

My suggestion to you is this: you have an access to this person that outsiders do not. If you have a Nobel-winner in the same building as you, who lines up for coffee with you or is sitting next to you at a meeting, you can talk about anything nontechnical at all. You can admire an item of clothing (what a cool tie! I love that ring!) or similar accessory (oh, you got the new phone/band/watch - is it good?) or comment on the weather, or how much you're looking forward to the presentation by the visitor, or just about anything other than the professor's research. I can't do that. How incredibly creepy would it be for me to email a Nobel-winner complimenting them on a tie or ring or watch worn in a press release picture?

They are indeed "just as human as we are" and because of that, your first interactions with them should be on that basis. Talk to them about the same things you would talk to anyone about. Don't burst out with a technical question you've been dying to ask. Just relax and be someone who while not a peer, has that inside access. Interacting properly with these people will include technical stuff - I can't so much as go to lunch without talking about technical stuff - but it will also include normal human stuff like "did you watch that game last night" or "were you stuck in that giant traffic jam yesterday" and the like.

I don't mind when people I've never met want to start conversations with me by asking my technical opinion, or sharing theirs. I love what I do. But if you want to form a true connection with your famous colleague, do it by emphasizing the colleague part first and letting the technical conversations arise a little more naturally. While I was thrilled to have Stroustrup tell me I should definitely write the "C++ as a first language" course for Pluralsight (I hesitated, because it's hard, but he encouraged me to do it and he was right, it's a great course in the end) it was actually slightly more fun to discuss the importance of caffeine to programmers and the sadly-neglected role of chocolate in that :-).