My boss tends to overuse the word "suppose". He'll say stuff like
I suppose you received my email?
Now, clearly there are more things wrong with that sentence than just using "suppose" in a context where "presume" or "assume" would be much more idiomatic: to start with, if he wanted to ask a question, he should have asked a question, instead of merely tacking on a question mark (or rather, the corresponding inflection, since this was spoken, not written) to the end of a statement. But let's just stick to word choice for now.
The dictionary definitions of presume, assume, and suppose make them seem pretty much interchangeable.
presume: to take for granted, assume, or suppose
suppose: to assume (something), as for the sake of argument or as part of a proposition or theory
assume: to take for granted or without proof: to assume that everyone wants peace. Synonyms: suppose, presuppose; postulate, posit.
But to my ear, suppose is the wrong word to use in most situations.
I suppose you are using Internet Explorer.
This is perfectly understandable — idiomatic, even, if delivered with the appropriate sneer — but to me, it means something quite different than
I assume you are using Internet Explorer.
However, I have been utterly unable to articulate what the difference is, at least not in a manner that gets my point across to my boss.