Based on the facts that these games have some similarities to games that are very popular here in North America and are played here in relatively small amounts already, and, with one exception, are already vastly popular in other parts of the English speaking world, these are games that we would love if we were exposed to them more and would become familiar with them.
Australian Rules Football
Wikipedia - Australian Rules Football
Major League
North America
Canada
Ontario Australian Football League
Northwest Pacific Football League
United States
Australian Rules Football Associaton of North America
United States Australian Rules Football League
Eastern Australian Football League
Mid American Australian Football League
Northwest Pacific Football League
South East Australian Football League
Cricket
Some Major Leagues
Cricket Australia (Covers all major Australian leagues
Friends Provident Trophy (England)
Cricket 20 (Covers Twenty20 Cricket all over the world)
England and Wales Cricket Board (Multiple Leagues)
New Zealand Cricket (Covers all major New Zealand Leagues)
Pakistan Cricket Board (Covers all major leagues in Pakistan)
Cricket Scotland (All Scottish Cricket)
West Indies Cricket Board (Covers all major leagues in the West Indies)
North America
Canada
United States
Team Handball
International Handball Federation
Major League
Handball Bundesliga (Germany - German only site)
Liga ASOBAL (Spain - Spanish only site)
North America
Canada
Canada Team Handball Federation
United States
Rugby League
Wikipedia - Playing Rugby League
Wikipedia - Comparison of American Football and Rugby League
Wikipedia - Comparison of Rugby League and Rugby Union
Some Major Leagues
National Rugby League (Australia & New Zealand)
Queensland Rugby League (Australia)
New South Wales Rugby League (Australia)
Kingstone Press Championship (UK & France)
New Zealand Rugby League (Covers all major competitions in New Zealand)
North America
United States
American National Rugby League
Rugby Union
Wikipedia - Playing Rugby Union
Wikipedia - Comparison of Rugby League and Rugby Union
International Rugby Hall of Fame
Some Major Leagues
Super 15 (Australia, New Zealand, & South Africa)
Aviva Premiership Rugby (England)
Guinness Pro 12 League (Ireland, Scotland, & Wales)
North America
Canada
United States