Canon.
Donna Noble
Companion of the Tenth Doctor, Donna becomes the Doctor's best friend. Although she enjoys teasing him more than being helpful, the Doctor can be fairly frustrated with her. Might also be because she pings that Time Lord sense that shouldn't be there. They're good friends now.
ever_so_plucky Rory Pond-Williams
Companion of the Eleven Doctor, Rory becomes a good friend of the Doctor. The Doctor treats him now as he would Mickey, meaning he's a bit harsh but does try to improve the way he thinks and sees the universe.
misterpond Amy Pond-Williams
Companion of the Eleven Doctor, the Doctor treats Amy like she is one of his own companions, compared to a future companion. A lot of that is due to Rory. He feels like he is competing against himself some of the time around her.
anybodyneedme Jack Harkness
Jack was his second companion after the Time War, and one the Doctor is always thrilled to have around. It's a bit obvious to him that something has changed. But, future stuff. The Doctor won't ask.
onlysayinghello Martha Jones
Companion of the Tenth Doctor, this incarnation of the Doctor doesn't know much about her yet. Besides the fact that she keeps a puppy named after William Shakespeare.
likestray_dogs El Dorado.
Bruce Wayne
His roommate and the head of Wayne Enterprises. The Doctor finds him interesting, and if he's worked out that Bruce is a vigilante crime fighter? He isn't telling.
BATMAN (NOLANVERSE) ■
whoiamundrneath Death (Didi)
While not the exact form of Death from his universe, the Doctor recognizes who she is. The two have bonded a bit over it and consider each other old friends. Too old.
SANDMAN ■
dontfearmebaby Vala Mal Doran
A military dressed woman who the Doctor met when she arrived. She's got her eye on his sonic screwdriver.
STARGATE SG-1 ■
valaunbound Leonard McCoy
A man from Earth who came into possession of a Tribble.
STAR TREK (2009) ■
doesnttrusttech