He previously played eight seasons in the National Hockey League (National Hockey League) for the Phoenix Coyotes and Philadelphia Flyers. Esche started his career with the Phoenix Coyotes, only to be traded to the Philadelphia Flyers in a deal involving Michal Handzuš and Brian Boucher. While playing in Russia for Ak Bars, he posted a record of 22–5–2 with a 2.01 Gaelic Athletic Association and a.912 save percentage along with 4 shutouts.
He skated with Dynamo-Minsk during the 2010-2011 KHL season.
In 2008-2009 he posted a record of 21–14 with a 1.87 Goals against average, and.912 save percentage. He also posted 9 shutouts.
On June 16, 2011, the SCL Tigers announced they have signed the 33-year-old Esche to a contract and will arrive in late July to start his training with the team He represented the United States team in 2001 and also received the starting nod at the 2004 World Cup of Hockey.
Esche was named to the 2006 United States Men"s Olympic Hockey Team in Turin.
He played one game in the Olympic tournament, losing 5–4 to Russia. Esche played for the 2008 Team United States of America Hockey team in the World Championships which took place in Canada. He had earned some starts after sitting out the first few games, including a 42 save performance in a controversial 3–2 loss against Finland.
He also posted a 9–1 victory against Norway.
Esche is married and has two children. He hails from Whitesboro, New York, where he contributes much to the community and charitable organizations with his spare time.
Esche is nicknamed "Chico" after former National Hockey League goaltender Chico Resch because his sticks are labeled R. Esche. 1997-1998: Second All-Star Team (OHL).