My personal opinion is that he is incognito; I see him clearly as someone who lives alone with a dog, doesn't like doing housework, grows zucchinis in the summer, hates shoveling snow, has arthritis in his knees, doesn't own a smartphone, his neighbors think him odd, he loves buying discount books at the flea market on Sundays, he's active on the internet under a plethora of pseudonyms and will likely release some of his coins when bitcoin reaches $1,000,000.
There are three possibilities:
1. He still has the private keys.
2. He does not have them or cannot access them (this includes his death without leaving them in inheritance).
3. He got rid of them on purpose, as a donation to the rest of Bitcoin holders. Recall his "lost Bitcoin is a donation."
Obviously I am referring to the million Bitcoins or so attributed to him for having mined them at the beginning. If Satoshi is still alive (or if they are still alive) I am sure he has a good amount of Bitcoin but that nobody links with Satoshi's name.
I think the most likely is option 3. Just as he started up Bitcoin for humanity and stepped away from the project I think at some point he purposely disposed of the keys to those Bitcoins, either for privacy, as a donation, or both. I find it hard to believe that someone as careful as he was would lose the keys and not have multiple backups.
Anyway we must hope those bitcoins will never move otherwise it could really be a big problem...