My DD was completely dependent and obsessed with breastfeeding, she would not eat anything but the boob at 1 year, so i waited to make sure she would eat! I finally got her to start eating around 15 months, and stopped at 16 months.
I was really scared because I thought it would be unholy hell, the days were not so bad (i cold turkeyed her) because I can take her our, take her to a park, let a little friend of hers come over. Do something I know would distract the hell out of her basically. Then night time came, and it was really hard on her, I have a computer in my room so I put baby Einstein baby lullaby on, and laid her on her belly and rubbed her back, or held her in my arms, or what ever else I could do to comfort her. I also started getting her special stuffed animals to snuggle with. and after 3 days of rough nights, she finally forgot about it.
My SOs co worker, said thats how her daughter did it, and within 3 days she was ok with it..that is what happened with my LO too!
I am currently nursing my 20 month old and my 3.5 year old. Neither are close to weaning (as far as I know), though my 3.5 year old does seem to nurse few times and for shorter duration some days. My 20 month old nurses less then he did at 12 months, but it is still frequent.
I don't think it's common for babies to wean at just over a year without some help from their moms (some babies will wean easily, some will be more difficult). I tried to wean my daughter (older child) at 11 months when I was getting ready to go back to work but she was not happy with that (and neither was I) so we stopped. While I was at work and pregnant, she nursed 3 times a day and that worked well for us. Now that I'm home through the day, she nurses about 5 times.