I am a 28 year old adult who converted almost 4 months ago, so I shall share my story. I was not raised in any church and I wasn't baptized as a child. My mother was a lazy Catholic and my father was a lazy Protestant and they figured I would figure G-d out on my own later on in life. But since I was never raised with any basic education in any faith, I decided that there was no G-d. As I got older I embraced this idea and did as much research into it as I could. I still have books by Christopher Hitchens, Richard Dawkins and Sam Harris. I dated an evolutionary anthropologist for some time as well and she took the stance that evolution proved there was no deity. A belief that she instilled in me. Despite knowing the 'truth' and feeling enlightened because I was above all those who were tricked into religion, I was miserable and longed for answers to life. I went through a long phase where I still didn't believe, but wished that I did. Then I developed a lengthy drinking problem that carried me through most of my twenties and took care of that need for knowledge. Temporarily. I went from longing for being one of the people I mocked and considered myself better than to being an angry non-theist drunk who not only didn't believe in a deity, but didn't believe in the possibility of one anymore. Fast forward several years to earlier this year, I'm drinking now just to stand the sight of myself. I was medically discharged from the military just over 4 years ago and back to not knowing what I want to be when I grow up. 4 years of military experience and 4 years of college and I'm working at Dunkin Donuts to make ends meet. I spent so much time being angry at a G-d I didn't believe existed and flushing my life down the toilet that I didn't take the time out to take care of myself. One day I had a feeling I had never felt in my life, and felt prompted to go to church. I went to a Catholic church very near to my house and felt the spirit. Finally I realized why people were going to church all this time instead of trying to drink as many years off their life as you could, like I had been doing. I knew I was on the right track but the Catholic church didn't have everything I was looking for. I am not bashing any church, I met some wonderful people there but I wasn't meant to be Catholic. I went online and requested a Book of Mormon. Shortly after that I got a phone call from this young gentlemen who said he wanted to drop off my free book and answer any questions I might have. These two young guys showed up, dressed all nice with nifty name badges, and a load of spiritual comfort for me. They explained the basics of the church and gave me my book and asked me to read, and pray, and ask G-d if it was true. I didn't have to pray. I knew right then that I had finally made my way home. I did tons of research into the LDS church, I learned their lessons before they even came to teach them to me. Within 3 weeks of them first showing up I was baptized. Within the first week of being in the church I received the Aaronic Priesthood and a temple recommend to do baptisms for the dead and I haven't looked back.
I spent almost 30 years looking in the world for happiness. Everything members who were born into the church were raised not to do, I've pretty much done. Except for murder. And the gay part. But every chance at what I thought was happiness that I could chase after, I did. I don't say these things in pride, or to reminisce about the good old days. I am flat out embarrassed for the way I lived the majority of my life. I was lost for long, and I think I hit bottom long before the missionaries found me. I figured that after I hit bottom I probably earned some time down there. I can tell you one thing for certain, there is no happiness in life without G-d, and the Savior was right about the world hating Him first.
I've thrown my whole life into upheaval. I've lost life long friends and have family that will have nothing to do with me because of my joining the church. I gave away hunderds of DVDs, sold my Xbox, deleted thousands of songs from my computer, shed tons of "friends" and now I spend as much time as I can doing church activities. I go out with our ward missionaries several times a week. I go tracting with them, visit less active members, do service for people, try to help them with teaching investigators, anything I can. I don't really match the poster for your standard LDS member, if there is one. I have partial sleeve tattoos, I'm almost 30 and not married, I don't have children, but I'm just living proof that the gospel is for everyone. I've been a lot of places and done a lot of living, and made more mistakes than most. I'm not bashful about my past, I'm more than willing to share every single speed bump I've hit in life if it helps someone else learn from my mistakes.
In my very short time in the church I've tried my best to reform my entire life. I'm moving in with a very good friend of mine in a few weeks, I'm going back to school to start a new career and hopefully I'll be able to attract a mate in a few years. I don't know how I'll do as a parent. I spend most of Sacrament Meeting giving the members kids starburst and watching as their moms try to figure out why their kids hands are red and sticky. I can't even get my cat to not jump up on the table when I eat, I am absolutely terrified about botching a child. But I know that there is no greater teaching available than the church, especially when it comes to matters of the family.
I am beyond thankful for that day those 2 young guys showed up at my door that day. Even though I don't really fit in with a lot of the people from my ward, I've been met with nothing but warm welcomes with no judging. I always have friendly faces greeting me on Sunday, calling me to invite me over for lunch, or asking if they can stop by just to see how I'm doing.
If I had to answer the question as to why adults convert, it's because there is no true happiness in life without the Savior.