There's a reason Senator Bob Dole came to be known as "Mr. Republican." From the Kennedy and Nixon administrations of the '60s up until the present day, Dole has been a widely respected voice in the nation's conservative party.
Kind of like Mitt Romney, he's one of those guys that Republicans really, really wish had become president.
Why didn't he? He had a chance to run against Bill Clinton in 1996. Not only that, he had the complete support of his party: Dole's nomination for the presidency was such a foregone conclusion that Clinton shouted him out in the 1996 State of the Union, just to be gracious (VIII.64.2). He even went on to deliver the semi-traditional "response" to the State of the Union, in which whatever party doesn't hold the presidency thrusts one of its chosen champion into the national spotlight.
So why didn't he beat the incumbent? Historical precedent wasn't to blame: Clinton was the first Democrat to be reelected since Franklin-freaking-Roosevelt. Dole's credentials certainly weren't to blame either: he served his country going all the way back to the Second World War, in which he survived some horrific battle wounds. After that, he served his home state of Kansas in the U.S. Congress for decades, chaired the Republican Party for a few years, and became a recurrent Republican presidential candidate (losing in various primaries to Ronald Reagan and George H.W. Bush).
When Dole's opportunity finally arrived, Bill Clinton was too shifty. The sitting Democratic president outmaneuvered the Senator in the 1996 State of the Union, casting himself as a family-centric candidate. He also criticized the media and entertainment industry. This was a killer chess move, because one of Dole's defining issues was being "anti-Hollywood" (just check out the opening line from his convention speech in 1996).
We can just imagine Dole sitting there thinking, "that's my line!" when he heard that one.
When Republicans couldn't make the election about character, "keeping your word" (Bob Dole's words from the debate), or entertainment industry sex and violence, they faced an uphill battle. The economy was strong, the national debt was shrinking, and Clinton's popularity numbers were steady: after the 1996 State of the Union, the Big Dog's approval rating never dipped below 50% for the rest of the year. (Source)
Seems like that "the era of big government is over" line did the trick.
Bob Dole had another, bigger problem working against him. At the time, Clinton still had a reputation as a young and fresh face, not to mention a cool-as-a-cucumber politician. People still remembered the sax. Most of all, they remembered how well he related to people at rallies and debates. In contrast, Dole was sort of awkward in public. He droned on in the presidential debates in a nasally monotone. Vote for me! Bueller? Bueller?
In modern politics, which are all about TV and hype, this sort of stuff matters. Dole lost by a comfortable margin in the November, 1996 elections, left the Senate, and now mostly goes on TV to cheer for Republican candidates.