Rafa was something of a curious bird. Clearly our most successful manager since the start of the Premier League (in terms of trophies [4 in his first 2 seasons, including no. 5, a second CL final, and a record number of EPL points to boot], game win %, regular qualification for the CL etc), yet he could only win over half the fans while somehow antagonizing the other half.
There are only 3 kinds of football. Beautiful football, effective football, and bad football. For the most part he had us playing effective football, which is difficult to elevate into the beautiful, and that somehow wasn't good enough. He made us defensively sound, even though he used the much-maligned zonal marking system to achieve it. He set a ridiculous number of club records, along the way elevating several good players into the realm of the supreme: Reina, Torres, Alonso, Carragher, Gerrard. I name the last two because he took them that step further - getting the former back into international football, and the latter permanently onto the shortlist of most feared midfielder and captain in Europe.
He was certainly arrogant, but most people seem to fail to understand that those with a winning mentality are arrogant as a side-effect; they are used to winning their way, so those who are not winning should shut up and listen. I would say that his inability to deal with the rifts he created in his squad when he marginalized players who did not show the necessary tactical discipline was his greatest flaw, and ultimately cost him his job and "our" CL spot (a CL spot that in all honesty had never really been "ours" prior to his arrival). He also revitalized the Academy. Above all he took absolutely no cr*p from Fergie, he really *got* the club, and as a result he'll always be close to the hearts of a large section of the supporters.
I'm not really going to go into "net spend" and his purchases after Hicks and Gillett bought the club, nor will I touch upon the supposed hanging of washing in public. All I will say is that one needs to remember that our erstwhile owners brought this upon the club, and while Rafa could have conducted himself better during those three seasons, he was working under conditions that sunk a certain highly-regarded manager who may yet manage England in a matter of months. Once one takes into account what those two did to the club, one might understand that we saw a dark side to Rafa's nature that under normal conditions would most likely never have surfaced. But I do not want to just gloss over this period, for it remains a black spot on his record, but too many people accuse him alone when in many cases he was simply the messenger.