Question
What age does your penis stop growing?
Answer
Your penis stops growing when you stop growing.
Data from studies of Bulgarian, Chinese, Indian and Italian boys show gradual increases in length of the penis between birth and 10 years of age, from about 3.5 cm to 5 cm. As the boys are growing, their penises are too.
At puberty, growth of the penis accelerates (the studies mentioned above show an increase from 5cm to 8cm between 10 and 15 years of age) and, as puberty ends, growth slows.

Data from a study of French men show that penis length is constant from around 20 to 40 years of age, and then starts to decrease. This might be because the penis becomes less stretchy with aging.
Stretchiness is important when it comes to measuring penises. Most of the studies of penis length make the measurements when it’s flaccid but stretched. This is because length of the penis is more variable when it’s either flaccid (and unstretched) or erect. (All the studies I referred to in this answer use stretched penis length, except the Italian one).
Are you worried about your penis size?
Plenty of blokes worry about their penis size, especially during puberty.
Like for all body parts, there’s a lot of variation in penis size. A review of scientific data, from studies with a total of over 15,000 people, shows that 95% of men have an erect penis length somewhere between just under 10cm to about 16.3cm.
Men’s penis sizes probably matter more to them than they do to their sexual partners. A study of more than 25,000 heterosexual men found that 45% wanted a larger penis. A similar study of around 1,000 men who have sex with men found that 34% wished their penis was bigger. Only 15% of a group of over 25,000 heterosexual women wished their partner had a larger penis.
For some men, it doesn’t matter that their penis is a normal size — they feel like it’s too small and they become preoccupied or distressed by what they think is problem. If this sounds like you, it might be body dysmorphia.