"Challenge Accepted" is an expression used to indicate that the speaker is willing to attempt completing a difficult task. The phrase is often associated with a rage comic character illustrated as a stick figure with crossed arms and a smug facial expression.
"Challenge accepted" began as a catchphrase for the character Barney Stinson in the television sitcom How I Met Your Mother. The earliest instance of Stinson uttering the phrase can be heard in Season 2, Episode 6 “Aldrin Justice” while announcing his intention to seduce an older woman. The episode originally aired on October 23rd, 2006.
[after Marshal infers his professor is tough on her grades because she needs to get laid]
Barney Stinson: Marshall, I've thought it over and I accept your challenge.
Marshall Eriksen: I didn't challenge you to have sex with…
Barney Stinson: Tomorrow, the cougar hunt begins.
The earliest known instances of the the rage comic character were posted in a thread by Body Building Forums member MK on November 12th, 2010, which included two challenge accepted examples (shown below).
On November 26th, 2010, the “Fuck Yeah Challenge Accepted Guy” Tumblr blog was created. On December 13th, the “Challenge Accepted” Facebook page was created, which accumulated over 145,000 likes within two years. On April 14th, 2011, a “Challenge Accepted” Meme Generator page was created, allowing users to make image macros featuring the rage comic character. On October 27th, FunnyJunk user JanFebMar submitted a rage comic showcasing photographs of a pumpkin carving depicting the character (shown below).
On June 21st, 2012, the Internet humor blog Smosh published a post titled “Best of the ‘Challenge Accepted’ Meme”, which featured several notable instances of the rage comics. Additional examples of the meme have been posted on the Cheezburger site Memebase.
The "challenge considered" rage comic character (shown below, left) is used to indicate that a task is being considered and "challenge denied" (shown below, right) is used to indicate that a task has been rejected.