Common first big projects

LOGO: Draw a house
BASIC: Fork GORILLA.BAS
Haskell: fibs and factorials
C: Reinvent a POSIX operating system
C++: Reinvent an STL replacement that is 5 mibibytes compiled and is also used by other languages as a GUI library, EVERY TIME

Scheme: metacircular evaluator
JavaScript: bloated OS GUI look-alike menus for your website
Go: another web server
Malbolge: something that compiles