Well, there's probably little point getting married if you don't want to live with a sexual partner, unless you just wanted the legal right to live in another country and that was the only way you could get it.
For myself, ever since puberty I've always felt a strong need for a faithful sexual partner who is also my best and closest friend, and I'm very attached to the idea of living together and sleeping in the same bed. I don't say it suits everybody. I've been through 3 failed marriages and a few out-of-wedlock failed relationships, but my current relationship is still very healthy after 3 years despite a lot of antagonism from external forces which we're striving to subdue, and I value that relationship very highly indeed.
As for marriage itself, I used to think it irrelevant because I think it's the way the couple feels about each other that's important, marriage has no direct bearing on that. Some folks have religious or other conformity-based reasons to marry, I don't understand those very well. But there are a few practical considerations. On the plus side, it tends to encourage the law and society in general to recognise and respect the relationship, e.g. potential sexual rivals tend to be less of a problem, people are more wary in general of trying to split you up, and if one of you dies then the surviving spouse usually gets a lot more rights to the deceased one's property and pension, and of course marriage to a foreign national gives you a better chance of living together in a country that has tight immigration laws. On the bad side, marriage can be an expensive thing especially if you opt for a big wedding with cultural expectations galore from various in-laws, and the ceremony itself could be a big strain. If you're receiving benefits, they might be cut, but in some places there's a tax break for married couples. And if the relationship finally fails, divorce is expensive too, and (in the UK at least) if your ex is likely to then suffer financial hardship, the law might decide that they can use you as a meal ticket forever after, regardless of your ex's behaviour. Clandestine affairs, desertion, even quite a lot of cruelty don't normally make a difference.
You might also want to marry so you can have children without any social stigma, though many communities these days won't judge you. Liability for child maintenance and custody / access rights are probably much the same whether you're married or not, but if you are married then arrangements for the children will automatically come to the attention of the authorities.