My DH had the snip when I was comparatively young - late 20s maybe? He is much older and had teenage children from his first marriage when we met. He was adamant that for a number of reasons, including serious health issues, he didn't want more children which was fine by me as I have never wanted them. I spent the first few years we were together on the Pill until I started to develop vascular migraine which was a contra-indication so we had to consider our other options. I can't remember how the subject of him having a vasectomy was first raised, but I think it was initially his suggestion. I would have happily considered sterilisation but at the age I was at then with no biological children, my GP refused to refer me.
I'm now in my 40s, still with him, still perfectly happy with my stepchildren, have no regrets about not having given birth and am grateful to him for sparing me the hassle of having to think about contraception.
Ironically, given that he had been in a serious relationship before me, the one thing we didn't discuss was the prospect of either of us wanting children from a future relationship, partly and most importantly I think because we were both 100% certain we didn't want children (or more children, in his case) and partly because we were both equally convinced that our relationship would last. Actuarially speaking, I am likely to be a comparatively young-ish widow given the age gap and his health problems (although it goes without saying I hope that doesn't become the case!) but the thought of some hypothetical future relationship didn't enter into the equation when we made the decision about our joint fertility based on our situation at that time.