Nate and Blair:
History: Nate and Blair had been together since they were twelve. They both thought of each other back then, as the person they were going to marry one day. When the show started though, only Blair was actually commited to that relationship. Nate had been in love with Serena and was obviously with Blair mostly because his parents wanted him to be. Blair was actually sensing that Nate was in love with Serena and didn't want to be in the relationship, but she was in denial of it. Blair wants to always control everything in her life and is actually driven by her dreams. Therefore, she couldn't end this because it was going to alter the way she had planned her life since she was young.
When Nate finally decided to stop letting his parents control his life, they broke up on the day of her birthday. Blair, then, was with Chuck and seemed quite happy and delighted. Watching her that happy, made her desirable to Nate again and he started pursuing her. After Chuck felt threatened and messed up, Blair decided she wanted to be with Nate without telling him what had happened with Chuck. Nate found out about Blair and Chuck through Jenny and broke up with her.
A year after that, Blair and Nate realise that they want to be together again, as their relationship seems natural and easy. Blair, though, soon realises that she loves Chuck more and wants to be with him. Nate and Blair haven't been together since then.
Conclusion: Blair and Nate know each other very well, even though it's not shown these days. What we tend to forget is that the way Nate treated Blair in the first season was terrible. He cheated on her with her best friend, used her to help his family and chose her birthday party to break up with her. The time they reunited, when he found out that she has slept with his best friend just like he had done to her, he didn't even consider the possibility of forgiving her, like she forgave him. In the second season, their relationship was much more healthy and Nate was a great boyfriend. But even then, it was obvious that they lacked the spark, Chair had. They loved one another but they weren't in love. And I'm sure that this ship is over. Since season 2, there hasn't been a hint that they might have feelings for eachother. They don't even share scenes anymore. Furthermore, his relationship with Serena, would make it akward if they actually got back together. How many times can these girls share the same man? What do you think?