A few stereotypes that I've heard about Stanford students are those imposed upon most Ivy Leaguers (note: Stanford is not technically an Ivy League school): namely, that we're all privileged white kids, with a substantial amount of us intent on being at the top of the pack (think: cut throat competition).
Here's the run-down: there's almost always a kernel of truth to any stereotype, but luckily for Stanford (and me!), in this case it's only a small kernel.
Being an international student myself who grew up in the Middle East, I can attest to the diversity of the Stanford population. The caveat - if you read the "official" calculation of Stanford's population - is that Stanford counts "Americanized" international students as "international" - i.e if grew up in the US with foreign parents you are considered international. I find that definition a bit of a stretch. However, regardless of your views of what constitutes international, there's a fair amount of people who grew up overseas at Stanford. Additionally, Stanford boasts itself on being one of the top colleges for students of color and those of latino/a origin (see this page for more info: http://admission.stanford.edu/student/diversity/index.html)
In terms of relative wealth, there are many privileged kids at Stanford, but not that privileged. Case in point: most Stanford students don't have a car (though that's partly out of convenience as well). Students commonly complain about the expense of food in Palo Alto. Additionally, I would say around 20-30{4a082faed443b016e84c6ea63012b481c58f64867aa2dc62fff66e22ad7dff6c} of the student population has a part time job to support themselves.
Last, let's talk about competition: My favorite part about Stanford is the lack of competition among students in most undergraduate departments. I say MOST rather than all, since my major is Sociology with a minor in philosophy (i.e I'm familiar with the humanities and social sciences). Based on what my friends in the more technical fields tell me, there isn't that much morale-killing competition in their departments either. I think part of that is West Coast culture, and part of that is purely Stanford culture. My brother went to Harvard and his characterization of their student population has led me to believe that Stanford is more collaborative than competitive compared to other top schools in the nation.