It's a double-edged sword, though. If you constantly appease a woman at your own expense, you're spineless. If you stand your ground, you're a heartless misogynist.
What works best for me is letting nearly everything go, simply because I really don't have strong opinions on many things. For the few things I do feel strongly about--no, I DON'T feel I need to bend to her will and will choose being right over being happy every time. Certain people may label me some expletive for not being respectful, but I don't care.
There was a study some years ago that had men agreeing with everything their wives said. What they discovered over the course of the study was that women's attitudes towards their mates deteriorated resulting in them becoming increasingly demanding and resentful. The relationships suffered, and not every couple was able to complete the study.
The simple fact is that having an opposing position to a SO is just part of you being yourself. By refusing to disagree, your SO loses part of the person he or she found initially attractive. The dynamic of the relationship shifts in such a way that the "alpha" will try to mold and shape or train the other and remain unsatisfied with the results, while the other has to endure abuse in silence. The takeaway? It really is better to be right than happy! 