For monogamous civvie relationships? Get tested first, then sure, go bareback.
I also second the suggestion to consider a vasectomy (in lieu of a tubal ligation for her), especially if you plan to have no additional children. It was a very non-invasive, it did not take long, and there was no blood.
And you will get a kick out of this: the urologist I went to had this gorgeous, young nurse and she thought I was kind of cute and sexy. The first time she got a look at it she dropped the metal pan of instruments she was holding. Being young I got quite a thrill out of it so I kept flirting with her and tucking with her so it took like 20 minutes longer than it should have. Lol. I am guessing she was used to seeing wrinkly McGray balls and not me. I don't know how many times I got her to drop stuff. Haha. Good times.
The other upsides to a vasectomy is you no longer need to keep the woman on any birth control pills, which can help with her hormones. It's a pretty selfless act which makes you a general A-1 guy in the eyes of a lot of women and who wouldn't like that?