Interesting question Cobalt. I honestly believe it's a combination of several factors:
1. She and her husband have been shady. No point in denying that. I don't think they're especially corrupt or wicked, but during their careers they've often played on the edges of what is legal or ethical.
2. Hillary is secretive and suspicious of outsiders- probably the most secretive and suspicious major politician we've had since Richard Nixon. Like Nixon, this is not all her fault; it's the result of decades of intense scrutiny and attacks (I'll get to that shortly.) But it lends itself to mistakes (the private server is a prime example) and conspiracy theories.
3. When Bill ran in 1992, Hillary presented herself as not just another First Lady but as a partner. As a strong woman, and up to that point probably the most visible of the new kind of liberated feminist that the 1960s gave us, she immediately became an anathema to social conservatives. She even more than her husband became enemy #1 and stayed that way until the rise of Barack Obama.
4. Now we combine the first 3 points: because of point #3 some right wing opportunists began to sell rumors and half-truths about the Clintons- they made a ton of money selling these to conservative groups eager to believe in the worst sort of accusations. Because of the Clintons' shadiness, and because of Hillary's secrecy, there was a lot of material for these guys to peddle: Whitewater, the Travel Office, Vince Foster, the FBI files, etc. Conservatives ate it up, but the rest of the nation barely paid attention. Until...
5. Bill got caught lying about Monica Lewinsky. This lie caused many of the other accusations against the Clintons to be more plausible, this time not just for the conservative base, but also for moderate Republicans and some independents. Most Democrats, however, didn't buy into it until...
6. 2008 and a desperate Bill and Hillary, losing to Barack Obama, made unfortunate comments and had surrogates attempt to smear him. This caused many Democrats to finally accept what Republicans had believed about the Clintons for years: that they were untrustworthy politicos interested in their own advancement.
That's a brief summary. Since 2008, 3 new scandals have emerged: Benghazi, the Clinton Foundation, and the emails. The details of these are less important than the fact that the public at large now has an ingrained view of Hillary as dishonest and corrupt, one that she will struggle to conquer. Since, as I have pointed out, I don't believe her to be particularly dishonest or corrupt, I think she can conquer this perception, but it won't be easy especially given her suspicion and secrecy which I already mentioned. Added to that, we are living in an anti-establishment period in which connections to corporations are in themselves seen as corruption.