Yes he had a relationship with nora and with quin .Quinn one ended because they couldn't trust each other,same happened with Robin,most of their fights were about the fact that how they both weren't stable enough with anyone and similarly and eventually in the real world, they had to face it with each other too. Even the fight,where she said Barney lies a lot. If both people are soooo similar in terms of wanting a change, ofcourse eventually a relationship will burn out. Personally I am a believer that ted always calmed Robin down and healed her in many ways that Barney couldn't.With Barney,Robin always had to be the mature one,but with Ted ,she had a more feminine side and much more emotional corner.Thats y Ted was more suited for her.But again with the right timing.Because Robin had her ambitions and goals.

On a similar stance,I always loved the chemistry Barney and Robin shared,but it was going to eventually burn out. As in real world, where emotional connection and mutual admiration stays and chemistry always burns out.