Just so we're clear, I don't think that all twin soul relationships are about big, romantic, Hollywood-ending, swoon-worthy, kissy-face couplings. Nope, sorry. (Read The Gemini Bond to find out why). (Yes, that was a shameless plug).
Still, there are some movies that remind me of a twin soul relationship in the way they portray two complete individuals who don't need the other person, but instead find that they are better people with their other half.
One of my favorites is Ladyhawke, starring a young Michelle Pfeiffer and a gorgeous Rutger Hauer. Matthew Broderick, looking not even twenty, is along for laughs (and it's not only for his 'here now and gone later' English accent).
In the movie, Isabeau (Pfeiffer) and Captain Navarre (Hauer) are victims of an evil spell cast by the Bishop of Aquila (John Wood). By night, the Captain becomes a black wolf, whose howls echo the loneliness of his soul, and by day Isabeau is a hawk who is cared for by the Captain. Eventually they manage to overcome the spell (I won't say how, but it's really cool), and confront the evil Bishop. Their reunion as two complete people is one of the most joyous I've seen.
Oh, and did I mention Rutger Hauer is shirtless? Yummers!