The Official Viserys Targaryan in the Game of Thrones was played by Harry Lloyed.
Updated June 2011: Harry Lloyed did a superb job as Viserys. Before Game of Thrones, he appeared in several tv shows including Doctor Who and Robin Hood.
When I read the books, Prison Break was still on tv so I thought of Wentworth Miller as Viserys.
Viserys Targaryan in A Song of Ice and Fire was the second son of Aerys II and was known as "The Beggar King". Viserys fled Westeros when he was 8 years old, along with his sister Daenerys, and spent fifteen years wandering the Free Cities until he arranged the marriage of Daenerys to Khal Drogo, hoping to buy Drogo's armies with her, and to use them to reclaim the Seven Kingdoms. Viserys, while ambitious, was also blind to reality - he saw himself as a rightful, victorious savior to the people of Westeros, due respect and adoration, never noticing that even his sister and his sworn knight Jorah Mormont scorned his petty, vindictive nature. Despite a constant loss of dignity and standing among Drogo's khalasar for his outrageous behavior, he continued to demand Drogo's aid.
Even though Viserys was supposedly in his early to mid 20's, I pictured him to be a young Cary Elwes as he was in the Princess Bride. He's aged now, like Michael Paré, who I thought of as Renly Baratheon, but still, blonde and youthful looking was how I thought Viserys to be, even though he had a mustachio. Perhaps someone like Wentworth Miller would make a good Viserys.