Coming from a Mexican family I can say that we are indeed an intelligent, hardworking bunch. 
Mexicans are stereotyped as lazy and stupid for the same reason that other immigrant populations (Polish, Irish, Italian) have been stereotyped as lazy and stupid throughout various periods of American history. Basically, it’s human nature to focus on disposition when evaluating other people rather than situation (we usually focus more on situation when evaluating ourselves, but that’s a different story). In other words, we see the fact that Mexicans are disproportionately represented in the lower class, and we often assume that the reasons can be traced to personality defects rather than economic and social circumstances. Since so many Mexicans are unskilled laborers, they must be lazy. Since so many Mexicans are uneducated, they must be stupid.
The reality, of course, is that many Mexicans are recent immigrants from an impoverished nation where they had no opportunities to better themselves. They are often uneducated and illiterate, and in many cases they do not speak a word of English. In order to survive, they must take the lowest-paying jobs available and live from paycheck to paycheck. Some manage to work their way up, accumulate capital, and provide an education for their children, who, if they are lucky, can someday move into the middle class.
I’m basically a third generation Mexican, which is why I’m enjoying the leisure of the Straight Dope at my very own personal computer and not digging a ditch somewhere for five bucks an hour. In a few months I’ll be the first in my family to graduate from college with a bachelor’s degree. I do not see this as a reflection of my personal strengths. I am merely lucky enough to have been born into a situation in which I was allowed to become educated without worrying so much about supporting myself.
My grandparents worked their entire lives as low wage, unskilled laborers. Through their hard work they allowed all of their children to finish high school and find good middle class jobs (which might not be so easy in today’s economic climate). And my parents, through their good middle class jobs, were able to save up enough money to put me through college. I’m practically guaranteed a straight shot through life, as long as the economy doesn’t do anything too funky in the next couple of decades. Even better, my kids pretty much have it made, and they haven’t even been born yet.
This is a common pattern for immigrant families. Now that a lot of Italians have been in America for two or three generations, many of the negative Italian stereotypes have vanished (do you even hear the term “dago” anymore?) A lot of them are educated, middle class, and able to speak perfect English, so there’s no real reason for the majority to stereotype them anymore, since they’ve become part of the majority themselves. I imagine that the same will be true for Mexicans, once they’ve had a few generations to assimilate. In fact, we’re seeing it now. Mexicans are starting to show up in the movies, on TV, and in other highly visible and prominent social positions. And you’ve got people like me popping up all over the place, proving that Mexicans can be intelligent, literate, and charming!