I'm getting the impression from reading the answers written by some of the real experts here that there are quite a few little packages that just tweak LaTeX2e's default behaviour a little to make it more sensible here and there.
Rather than try to pick these up one by one as I read answers to questions (and thus risk missing them), I thought I'd ask up front what LaTeX2e packages people load by default in (almost) every document.
As this is a "big list" question, I'm making it CW. I don't know if there are standard rules across all SE/SO sites for such questions, but on MathOverflow the rule is generally: one thing (in this case, package) per answer. I guess that if a couple of packages really do go together then it would be fine to group them.
This is perhaps a little subjective and a little close to the line, so I'll not be offended if it gets closed or voted down! (But please explain why in the comments.)
Also see our community poll question: “I have used the following packages / classes”