An epic hero must meet certain criteria which makes this a really difficult question...
"The epic hero illustrates traits, performs deeds, and exemplifies certain morals that are valued by the society from which the epic originates. They usually embody cultural and religious beliefs of the people. Many epic heroes are recurring characters in the legends of their native culture. Epic heroes are superhuman in that they are smarter, stronger, and braver than average humans. An epic hero can also be a warrior of some sort who performs extraordinary tasks that most find difficult. This hero is strong, smart, and brave."
A modern version of this could be someone famously doing good throughout the world - a famous soldier or celebrity, perhaps. I hate to say it but Angelina Jolie embodies many of the qualities described in the wiki-definition: She is dedicated to helping refugees throughout the world, adopting children from all over, and donating to charities supporting world peace. I am sure people could easily argue against her, but she continues to have and share experiences, epically in a sense, which is why I use her as an example.
I would say an "ordinary" person can not do such things as she has been selected as an Abassador for the US (most people do not receive this honor) and she has millions of dollars to spend to do her deeds (most people do not).
There's also Oprah....ha ha! You could probably make a case for her as well, but I would go with A. Jolie.