If you went to a Harvard, a Stanford, an MIT or a Texas A&M, and you happen to end up with more money than you know what to do with, you might be inclined to give a big pile of it to the university that got you started. And while that's a noble sentiment, you shouldn't. These places will continue turning out talented graduates no matter how much money you give them: you should give your money to a less-well-endowed institution, so that a larger number of students can get the same educational opportunity you had. Maybe your spouse went to a small liberal arts college. Maybe there's a place right down the road from your mansion that could use your help. But MIT and Stanford don't need your money, and they won't do much good with it.
A bit of data: Harvard's endowment amounts to $1.7 million per student. With a reasonable return on endowment investment, hey could quite literally abolish tuition forever if they wanted to. Just across the river is Boston University, a really excellent institution with a strong research focus and really great graduates, ranked #42 by US News. Its endowment per student is 1/25th of Harvard's.
Donating money toward improving education is a worthy goal, but don't get sentimental. Put the money where it'll do the most good for the most people.
(Full disclosure: I'm a professor at a liberal arts college whose endowment per student is mediocre at best.)