Harry's first relationship was a fiasco. But his second was quite a bit different.
Cho Chang, a pretty girl from Ravenclaw, and Harry once had a brief but difficult relationship. Harry had a crush on her that even propelled him to ask her to the Yule Dance during his fourth year. She was forced to decline as she already had a date with Cedric Diggory. Her relationship with Cedric grew as the year went by. It was Cedric who was later killed by Peter Pettigrew (by order of Voldemort). Cho tried to get closer to Harry during Harry's fifth year, but things just weren't meant to be. Cho seemed to want to be with someone who knew and understood how she felt about Cedric's death, but Harry began to grow tired of her constant talking (and crying) about Cedric. He was there when he died, he didn't need the constant reminder. The last straw came at the hands of Cho's friend, Marietta. Marietta told Umbridge about the secret D.A. association which of course led to more trouble for Harry.
By the end of the fifth year, it appeared that Cho had found someone else. Thus, it seems that the Cho/Harry relationship was over before it ever really took off. In Harry's sixth year, the two had no interaction besides occasionally seeing each other from afar. However, Cho was among those who returned to Hogwarts for the final battle. In fact, she seemed quite happy to see Harry, and even offered to accompany him to the Ravenclaw common room to view the statue of Rowena Ravenclaw. Ginny, however, insisted that Luna take Harry instead.
Ginny, the younger (and only) sister of Ron Weasley, had a crush on Harry the minute she met him. Because of this crush, she was barely able to stand being in the same room with when she went to Hogwarts without doing something embarrassing. Ginny nearly lost her life to Tom Riddle during her first year at Hogwarts as she had virtually become the prisoner of his enchanted diary. Harry managed to save her just in time.
The awkwardness changed after all this and eventually the two became friends. But, Harry often seemed oblivious to her as Ginny had her own friends her own age. Harry neglected to speak to Ginny regarding Voldemort and possession when she was the most obvious person to talk to. It seemed at the end of the fifth year, no matter what "furtive looks" Ron sent Harry's way, these two would merely remain friends.
However, during Harry's sixth year, he began to get jealous of the boys Ginny was dating. It seemed that Ginny was indeed a very popular girl, and had her share of boy to pick from. Harry's crush continued through the year, and finally made itself public when he kissed her after a Quidditch match (one he was not able to attend due to detention). Ginny was happy to begin dating Harry, as she had apparently never really gotten over her own crush.
After Dumbledore's death, Harry decided it was time to isolate himself as much as possible from those he cares about. He broke things off with Ginny in order to keep her safe. He held to this promise as the summer following his sixth year progressed, though he did let her kiss him while he was at the Burrow for Bill and Fleur's wedding. This was the last moment they spent alone before Harry, Ron and Hermione were forced to depart and head out on their search for the Horcruxes. During the search, Harry often thought of Ginny and sometimes looked for her dot at Hogwarts on the Marauder's Map.
Meanwhile, Ginny was busy with her own war as she, Luna and Neville kept Dumbledore's Army alive and strong at Hogwarts. Their numbers began to diminish once Luna was taken. During Easter holidays, Ginny was safely taken to her Aunt Muriel's to be with the rest of the family. She returned to Hogwarts for the final battle, along with her entire family. Her family insisted that she not fight as she was too young, but she did eventually join the battle anyway.
After the battle, Harry and Ginny were eventually married. Ginny played with the Holyhead Harpies (an all-female Quidditch team) for a few years before becoming the senior Quidditch reporter for The Daily Prophet (source). Harry and Ginny had three children: James, Albus Severus and Lily.