No, it does not take many years of burning to develop skin cancer.
Especially if you have light skin, light eyes, or a family history your chances are much greater to develop cancer.
I tanned in a bed for less than 2 yrs., not too much, never burnt in the tanning beds, I have fair skin and blue eyes, no family history, and I'm 37. Last year I developed a mole that had to be removed because if left alone it would have become cancer. The biopsy showed it had changing cells so a complete removal was done, a deep excision leaving about a one inch scar. I can only attribute this to the tanning bed since it was in an area that never got natural sun. My husband and I both noticed the mole within 24 hours of eachother, that's what made us suspicious of it.
Tanning, either naturally or artificially, is damaging to the skin. If you want safe color, go to the spray tanning booth or use self tanning creams.