Can man

The Can Man is a mysterious figure who appears to be closely following the companions of the Doctor for curious reasons yet to be discovered.

Appearances
The first time we see The Can Man is during the the Fourth Doctor's mindbending duel with Morbius (The Brain of Morbius). During the duel we see all the prior incarnations of the Doctor we are familiar with, along with some unknown faces, suggesting that these faces are also previous incarnations of the Doctor.

Among the unknown faces shown is a face that looks like that of the Can Man. If we are to believe that the unknown faces are previous incarnations of the Doctor then it means that the Doctor and the Can Man share the same early life. Curiously, when the Can Man's face appears in the duel, the minbending device burns out and both Morbius and the Doctor are injured. This suggests that the Can Man incarnation is especially powerful.

2005
The next time we see the can man is in 2005, during the 9th incarnation of the Doctor (Aliens of London). He's invited into Rose's house among with various other people (including Bau), meaning that he found some way to get close to Jackie due to her connection to the Doctor/Rose, much like Elton did (Love & Monsters). During this time we see him typically holding a can, and he's shown to be eavesdropping on the activities of Rose, Mickey and Jackie. We know he's not just looking into their conversation by accident, as when Mickey closes the serving hatch to block his view, he quickly moves to the open door, which Mickey has to then shut also.

2021
We next see the Can Man during the Doctor's 13th incarnation. Again he is shown to be spying on the Doctor's companion as an unsuspecting neighbour with his can in hand, only this time the companion he's spying on is Dan instead of Rose. He knocks on Dan's door four times during Halloween saying "Trick or Treat". When asked his age, he doesn't answer the question, responding with "what's the difference?", perhaps to avoid lying to him as (being a timelord) his age is probably centuries old by that point. He then looks up at the house briefly, and shortly afterwards we see Dan's house shrunk, taking an upper wall of the neighbour's house with it. This suggests that he not only knew/suspected that something would happen to the house, but that he even had an idea of the exact part of the house the change would come from. Whether he caused it, was trying to stop it, or was merely observing is unknown.