It's heavily implied that Shadow is Relm's father.

Shadow's dog Interceptor, who seems to dislike most people, likes Relm.

Relm: What a cute doggy!
Shadow: Get away. He bites.
Strago: Go to your room!
Relm: I will not! What a fussy old man!
Strago: Please.... leave us!
Relm: Well... all right...
Strago: Hoo boy... Seems to like your dog...
Relm: Here boy!
Strago: This is terrible...
Strago: Sorry.
Shadow: No problem. The dog usually doesn't like people, though...
Further, if Shadow dies at the Floating Continent, Relm takes his place in the Cave in the Veldt. If Shadow is rescued at the Cave, however, he will be taken back to Thamasa. Further still, Shadow and Relm are the only characters who can equip Memento Rings, which bear the description [Departed mom's love protects against fatal attacks].

They are also linked by dreams; Shadow can have a series of dreams; Relm will have a dream should Shadow die. In this dream, Relm see her father leave. Shadow's dreams detail his former life; we see partners in crime Clyde Arrowny (Shadow) and Baram off living the life of crime. Eventually, Baram is wounded, and asks Clyde/Shadow to kill him so he won't be captured. Shadow is unable to go through with this. Clyde eventually ends up in Thamasa. Later, he leaves, saying he wants a woman (presumably his wife and/or lover, Relm's mother) and her child to live in a happy place.

More could be listed, but, really, the connection is fairly apparent.