Median family income is about $52k (as of 2014, might be smidge higher now). About 28% of households are over $75k (and hence 72% below) so it's sort of hard to call anything over that "middle class" by any reasonable standard.
But almost everyone with a job, even people making $250k (I personally know plenty of people like this) considers themselves "middle class". I even know a mid-6-figure income person who once told me he considered himself "working class"...
Most people making $250k a year would probably categorize themselves as upper-middle class to signify that they aren't "rich" but to also recognize that they live better than the vast majority of people. People in that income range generally can afford average homes in the nicest neighborhoods. Send their kids to private schools. Pay for their kids college. And a whole slew of other opportunities not available to average middle class people.
Typically middle class starts as you say in this country at around $40k. Where depending on family size we can generally say someone is not in a state of poverty. Thats all middle class means initially.
Then beyond that we generally assign cutoffs based on earnings relative to the total working population. Because generally we are interested in our wealth with regards to other people. That makes sense since the ultimate purchasing power we have rests with how many competing buyers we can outspend for limited goods.
Pew research defines middle class for the country at large as anyone not in the top 20% or bottom 20% of earners. The other major relevant factors you always have to consider are where you live and how many people that income is supporting. At large ignoring location and family size, middle class is generally around $40k-$140k currently.
The thing that really skews the thinking and makes almost everyone feel middle class, or in other words not feel rich, is that the difference earnings between someone in the top 5%, top 1% and top 0.1% are drastically different than the difference between a top 20% earner and a middle 50% earner.
Of course the other factors that go in to defining middle class and upper class with regards to wealth are, raw net worth and consumption. But generally we are more enamored by income as a means of differentiation.
I would say upper-middle class, from an experience standpoint, begins when you can do things like. Max out your $401k. Easily save 10% or more of take home post tax money a month on top of a full funded retirement. Easily maintain a 3 month + emergency savings. Buy any necessary item short of a house without ever have to go into debt.
I think another interesting metric when considering who is middle class along the lines of consumption would be to look at savings rates. One potential luxury of being middle or upper middle class is that in theory you may never have to live paycheck to paycheck or borrow money for basic necessities and minor luxuries.