What did the ancient Egyptians think of Khufu?

I think your question has many parts to it depending on what social class you are looking for. Typically, those in power feel one way over those that are enslaved. I have found evidence though that Khufu was thought of as a greedy, self serving, malicious, leader. Based off the article below who cites primary sources

Khufu is often described as a cruel leader. Contemporary documents suggest that unlike his father he was not seen as a beneficent ruler and by the Middle Kingdom he is generally described as heartless ruler. In the Westcar Papyrus he is depicted as being keen to increase his own power and ensure the continued rule of his family, but is not as a particularly cruel monarch although he does offer the life of a criminal to test the skills in resurrection of a magician (which is often quoted as evidence that he was evil). -Source Ancient Egypt Online

I also found this:

Although King Sneferu was remembered as a benevolent and beneficent ruler, Khufu is believed by some to have been a more ruthless and cruel despot. He was rumored in later times to have been prone to enjoying the fantastic stories of the reigns of his predecessors, as well as tales of magic and the mystical. His fame lasted throughout Egyptian history and he still had a funerary cult as late as the Saite Dynasty (26th Dynasty). Of course, whether or not he was a cruel ruler, he did command a tremendous ability to organize and mobilize worker. -Source: Guardians Of Egypt

The one thing you should always remember when studying history is look at who is writing the primary source. Conflicting reports can be found about almost all leaders what matters is can you group the opinions together based off of social status, ideological beliefs, location, etc, etc.

Why the idea of Khufu being a tyrant is common

Herodotus said so, in his "Histories", Book II. The fulltext is here. The section concerning Khufu is the last quarter of the book or so, starting with the paragraph "Till the death of Rhampsinitus ...".

According to wikipedia, Diodoros Siculus made similar claims about Khufu, but Diodoros, living 400 years after Herodotus would have been aware of Herodotus' claims.

Now, when it comes to ancient Greek historians, writing about things they could not possibly have known, I would urge extreme caution. Both of them, Herodotus and Diodoros, lived more than 2000 years after Khufu died, literacy was less common at the time than in the last 2000 years and they would have known much less about Khufu's time than we know about events 2000 years ago (e.g. about Diodoros). Being ancient Greek historians, however, they adopt a paternalizing tone and attempt to lecture us about anything and everything.

What was Khufu really like; what did his subjects think of him?

Impossible to know. He was a well-established king; he - or more likely his vizier (tjati) - oversaw many great building projects including one that would remain the tallest man-made building for almost 4000 years. Presumably, his subjects thought that he was the king (actually, the Pharaoh, hence a living god) and that it was appropriate for them to follow his orders. There is no evidence that he was particularly cruel (for an absolute ruler), especially not in the ways that Herodotus etc. detail.

According to wikipedia, Khufu had a more extensive mortuary cult than his immediate predecessors and successors, suggesting some level of popularity. It even seems to have been revived later, in the New Kingdom.

What is wrong with Herodotus' account?

Several things:

• Herodotus account is not supported by any independent evidence.
• Herodotus gets Khufu's name wrong (calling him Cheops) to the extent that his Egyptian contemporary Manetho, who was familiar with Herodotus' work, did not recognize it (see the wikipedia article).
• Herodotus links his alleged cruelty to the pyramid and slave labor used in its construction, while all archaeological evidence suggests that the pyramid was constructed by skilled workers, perhaps even voluntary labor.
• Herodotus professes to know an awful lot of detail about the time while the ancient Egyptians themselves were obviously only aware of a few vague facts. For instance, Khufu's mortuary cults were given up several hundreds of years after his death, the structures decayed, and the Sphinx, that belonged to the complex was buried in sand. It had to be dug up several times in ancient times; the Dream Stele added to it on one such occasion makes no mention of Khufu or his funerary complex.
• Herodotus recounts that he gained this information from Egyptian translator (who, as Herodotus says in the source cited above, read some of the inscriptions to him). You can't help but wonder whether ancient tourist guides were as skillful in manipulating gullible tourists as modern ones.
• Some of the stories that Herodotus relays about Khufu are laughably ridiculous. For instance, he says, Khufu forced his daughter into prostitution in order to raise more money and satisfy his greed. First, Khufu was an absolute ruler, and if he saw the need to raise funds, he would have found a way to do that without involving his immediate family. Second, Egypt at Khufu's time did not have a money-based economy. All evidence suggests that taxes were collected in commodities (and perhaps forced labor) and soldiers and laborers were supplied with food directly instead of receiving a monetary wage and buying necessities from it.

But why were Herodotus & Co. so wrong?

The wikipedia article suggests multiple reasons: propaganda and defamation on the part of the Greeks, a dislike for huge building projects (for which the pyramid certainly qualifies) in later times, or a misreading of the character denoting Khufu's name (originally read "Khufu", "the protected one", but later "Shufu", "bad luck", "sinful").