Robert Baratheon is the sitting king at the start of the Game of Thrones series. The story was based on the real life War of the Roses, Robert Baratheon is obviously heavily based on King Edward IV of England. Robert's Rebellion at first seems a little odd that the Iron Throne did not go to House Stark since the war was sparked by the murder of Rickard Stark and his eldest son Brandon Stark. However in the books, Robert is the grandson of Princess Rhaelle Targaryen (who married Ormund Baratheon) and she was the daughter of King Aegon V. This makes Robert 2nd cousins to Rhaegar and Daenerys, and gave him more "right" to the throne than House Stark which had no blood of the dragon.
Robert was suppose to marry Lyanna Stark and fought the war to "save" her. When she died, he married Cersei Lannister who actually was suppose to be a bride to Rhaegar but the Mad King Aerys' distrust of Tywin Lannister caused him to snub her and give that role to Elia Martell. If the Mad King had not done so, then House Lannister would have supported House Targaryen under any conflict which ironically would have kept them on the throne. While a wonderful political match for House Baratheon, Cersei was not a good bride and gave him false heirs. King Robert was a terrible husband on another hand with his own bastards, so I can't really criticize one over another.
While Robert and Ned Stark were best friends, their friendship was often strained. Robert had a vicious dark side when it came to keeping the Iron Throne. Robert closed his eyes on the Targaryen children murders committed by House Lannister which caused a huge friction between him and Ned. They repaired their friendship but that was later tested again when Ned Stark refused to let Robert assassinate Daenerys without boldly voicing his opposition.
While Robert Baratheon has many qualities to dislike, I liked him over-all. Compared to the next line of kings and pretenders, he did a good job. Though it is a shame he killed Rhaegar and indirectly put Jon Snow into a false life of being a bastard. While the show and books have not yet confirmed that Jon Snow was trueborn, I think so. If Jon Snow was a bastard, Robert would have little reason to want him dead especially with better Targaryen heirs alive. However if Jon Snow was the trueborn son, then by law (not conquest) Jon Snow is the true king.