There are many twin registries all over the world! Here are links to some of them.

USA

California Twin Program

Michigan State University Twin Registry

Mid Atlantic Twin Registry

Minnesota Twin Family Study

Missouri Twin Study Program

Pennsylvania Twin Registry

Twin Research Registry at SRI International

Vietnam Era Twin Registry

Wisconsin Twin Research

Australia

Australian Twin Registry

Queensland Twin Register

Asia

Chinese National Twin Registry*

Healthy Twin Study (a.k.a. The Korean Twin-Family Register)

Keio Twin Registry (a.k.a. Tokyo Twin Cohort Project)*

Sri Lanka Twin Registry

Europe

Berlin Twin Register Health Twist*

Danish Twin Registry

Finnish Twin Cohort Study

Hungarian Twin Registry*

Italian Twin Registry*

Murcia Twin Registry

Netherlands Twin Register

Norwegian Twin Registry*

Swedish Twin Registry

TwinsUK

*website is not in English