For the meaning "inside", 裏 or 裡 is the traditional form (as @Ringil has pointed out, 裏 is the proper form in the standard of Mainland/Hong Kong and 裡 is treated as a variant; but in Taiwan the situation is reversed), and 里 is the simplified form.
For the meaning "mile, kilometer, li (Chinese unit of distance)", 里 is the only correct form in both traditional and simplified Chinese. So be careful: 公里, 里程 cannot be written as 公裏(裡), 裏(裡)程 – That's wrong, wrong, wrong.
A few more comments
Duan Yucai's Commentary on Shuowen Jiezi wrote
The layer inside clothes. And the meaning is extended to generally "inside". The radical is 衣. Sounds 里. Consonant like 良 and vowel like 止.
So basically speaking, 裏 and 裡 both comprise 衣(礻) and 里. There's no difference between these two characters – if any, in my opinion, 裏 is a more "proper" form to exhibit the ideogram of the ancient scripts.
居也。从田从土。凡里之屬皆从里。良止切。Dwell. With radicals 田 and 土. In the category of 里 all characters have 里 as the radical. Consonant like 良 and vowel like 止.
In modern Chinese, 里 is generally related to the distance unit li, kilometer or mile (sometimes it's written as 英哩 or just 哩). However in ancient Chinese, it has various meanings such as dwell, alley, lane, community, village, li (Chinese unit of distance), and hometown. Just note that in these cases, it should never be written as 裏 or 裡.