One of the biggest problems that plagues any relationship from succeeding, or even beginning, is selfishness.
Merriam-Webster defines it thusly:
1: concerned excessively or exclusively with oneself: seeking or concentrating on one's own advantage, pleasure, or well-being without regard for others
2: arising from concern with one's own welfare or advantage in disregard of others
— self·ish·ly adverb— self·ish·ness noun
It is rather impossible for us mere mortals to be 100% self-less 100% of the time, but we can sure try. In a relationship, any relationship, the other person, or, more importantly, the couple, should be put before the individual as much as possible.
This concept requires compromise. You will not always get your way, nor should it be about getting your way. You don't have to have the same level of enthusiasm for something as your partner might, but supporting them and their choices/activities/ideas will likely lead to them doing the same for you in return, and both will mutually benefit. In other words, a relationship should not be based on give and take. It should really just be give. You will receive in return, but that should not be your goal.
William Wordsworth put it this way:
The world is too much with us; late and soon,
Getting and spending, we lay waste our powers.
A poor man can be selfish and a rich man generous, but a person obsessed only with getting will have a hard time finding peace in his life.
Elder William R. Bradford said "Where there is selfishness, the Spirit of the Lord is absent."
Certainly, we want the Spirit with us as we make and maintain one of the biggest decisions of our life, right?
President James E. Faust said
We torture our souls when we focus on getting rather than giving . . . One of life's paradoxes is that a person who approaches everything with a what's-in-it-for-me . . . will lose the fulfillment and the happiness that a person enjoys who shares his talents and gifts generously with others.
Elder Neal A. Maxwell: A narcissist society, in which each person is busy looking out for number on, can build neither brotherhood nor community.
Also from Elder Maxwell, "The severely selfish use others but do not love them."
There are few things worse in a relationship than feeling used. Whether it be like you feel like you're being courted because of your car, your money, your status, or, worse of all, your body, to not be valued for your whole soul makes you feel unimportant and worthless. Completely.
"No one has the right to make you feel inferior without your consent." (Eleanor Roosevelt)
Selfishness has devastating consequences. As I look back, most of my romantic relationships have ended due to some degree of selfishness, either on my part, or my partner's, or both. I've even lost friends because of selfishness. Worse still, "[s]elfishness is actually the detonator of all the cardinal sins." (Elder Maxwell) This severely damages the relationship one has with our Heavenly Father. Those who bend to their own apetites and desires rather than those of others burn bridges and make it difficult for real love and trust to develop.
I'm not saying that both partners have to be so selfless that they, metaphorically, stand at a door together and say "No, you first, I insist" for eternity. Someone has to go through that door, but with their partner following close behind.
Again, mutual respect, love, compromise, decisions, and, especially, communication should be become key components of any succesful relationship. I'm certainly not perfect, and this is just as much for myself as it is for anyone else, but I'm constantly trying to better, and so should you be.
As Joseph Smith said, "Let every selfish feeling be not only buried, but annihilated."
All quotes can be found here and here.