Don/Jessica (CSI NY) - they were really good together, even when they were "just" partners, but when she died and he carried her out of the cafe, I just cried.
Wesley/Fred (Angel) - I've seen the whole series couple of times now, but the last few episodes of Season 5 make me cry every time I watch them.
Clark/Lana (Smallville) - normally not a couple I consider a favorite, but their very final scenes in "Requiem" brought me to tears. It was a cruel twist of fate of involving Kryptonite (since I considered her Clark's hart-, hart Kryptonite for a long time - too long exposure will kill you), but on the other side it made way for Clois ;)
Aaron/Haley (CM) - sure, they had meer downs than ups (at least what we saw on screen), but witnessing her death via phone (and with the rest of the team listening in) was sad and definitely the cruelest death on CM so far.
Chris and Adriana from The Sopranos...I know most people probably don't even really think of Sopranos couples as depressing but here are my reasons: Chris tried to stay clean for Adriana and then when he found out she was snitching he seemed hart-, hart broken about having to choose between her and the family, probably out of a sort of father figure fear of Tony he chooses the family and they kill her. Eventually the man he gave up Adriana for (Tony) ends up killing him because he doesn't want to deal with him anymore...saddest ship ever, yet also one of my favorieten if that makes sense.
10/Rose from Doctor Who. The first time they're separated is heartbreaking. Then the seconde time at Journey's End, they're reunited only to be separated again. Rose gets a happy ending with The Doctor's clone, but the poor Doctor has to lose Rose again.
Wesley/Fred from Angel. First Fred is killed and a demon named Illyria infects her body. So Wesley has to see the face of the woman he loves everyday, but it's not her. Then Wesley dies a few episodes later. He dies in the arms of Illyria and while he's dying, Illyria pretends to be Fred.
Cordelia and Angel also had a sad ending. So did Willow/Tara, Xander/Anya, Paul/Echo, Topher/Bennett, Billy/Penny etc. u get the point, most Whedon couples end in tragedy. I also found the end of Spuffy to be kinda sad. Spike didn't believe Buffy really loved him in the end. I know he gets brought back to life, but it was still sad. Picture below is of Wesley and Fred.
At the end of No Exit, they part on bad terms (Jo is upset thinking about her father's death and lashes out at Dean, I think this lowers his opinion of her a bit). The last time we see Jo is in Born Under a Bad Sign when the Meg demon, possessing Sam, goes after her. Dean shows up and fights Meg, then he and Jo have a sedate disillusioned parting.