Here are my favorite websites:

Mathematical competitions:
Asian Pacific Competition
Iberoamerican Mathematical Olympiad
The William Lowell Putnam Mathematical Competition
Balkan Mathematical Olympiad

Country Mathematical sites:
Argentina
Australia
Belgium
Brazil
Bulgaria
Estonia
Germany
India
Ireland
Mexico
Moldova
New Zealand
Netherlands
Norway
Peru
Poland
Romania
USA

Personal websites related to Mathematics:
Kiran Kedlaya
Tom Verhoeff
Hans Vernaeve
Naoki Sato
John Scholes
Gabriel Carroll
Andrei Jorza 
Valentin Vornicu