My shippings are floating around in another thread somewhere, but what the hey... I'm a girl and I wuv teh shippings, so I'll post again.
Rolf/Anna- I think there was potential for some sparks. Plus, their sprites match.

Ultimately I don't see either as being interested in a long-term relationship other than to be close friends.
Rudo/Amy- Just in case I have to give a
logical explanation as to why, I figure their differences complement each other. Amy's not strong and Rudo's a giant man-shield, thus he's getting injured frequently, so cue cute doctor. Rudo was a family man and Amy comes "from a normal home," so there seem to be some similarities in having or wanting a stable home as well. Or, you could just follow my ongoing fic.

Kain/Nei- It falls under the category of "almost canon" since it was mentioned in at least two Sega publications. Plus, it's really sweet. Well, and ultimately tragic.

Wren/Mieu- NOT romantically. I'm guessing they continued to be close companions for a very long time, even after the events of PSIII.
Nial/Alair- It's by far the least logical marriage option in PSIII, but I'm going to give Alair some credit for seeming the most excited of all the PSIII women about being chosen. Perhaps there was much more going on behind the scenes than what we were shown in the game.
Crys/Kara- Two strong personalities that come from warring clans up until the time of their adventure... it's your classic love/hate relationship.
Rune/Alys- This is a highly logical pairing to me. Maybe not the most exciting or romantic, but it makes a heck of a lot of sense.
Hahn/Saya- Canon.
Chaz/Rika- Canon.