I nursed my kids until they were 3-plus. My daughter did the same with her children. If a mother is open to allowing weaning to happen in its own time, it's lovely and easy.

Allow me to tell you a short version of a great story. The cultural anthropologist (and breastfeeding expert) Dr. Katherine Dettwyler was in Africa with a teenaged boy when they suddenly came upon a lion. Terrified, they froze, and the boy instinctively reached up to feel Dettwyler's breast. The lion moved on and all was well. She understood that this wasn't remotely sexual for the boy; it was him going back to his childhood. The breast is the ultimate comfort object.