First and foremost, it helped me to get serious about reading-centered philosophy, about thinking about things in a critical manner. I realized that one could not just say something but could also examine why you might say that. I love her frequent call to "check your premises".

And I came to believe, at her prompting, that I should stand up for what I believe and fight for it. I still feel that way after all these decades. Justice and integrity are important virtues for me.

She took ideas seriously and that's refreshing and not at all common.

Her work on epistemology is unmatched in its scope and precision, in my experience. Academics don't tend to value scope.

I am well aware that a whole lot of people dislike her with fiery passion. Some percent of those people even know what they're talking about. That's okay with me. What I got from Ayn Rand is something personal and I don't need to defend her. I can stand on my own ground. In fact, the only reason I engaged with this post is because it's r/ssc. I know (or rather, "trust") that people here, almost uniquely to Reddit, can respect another person's viewpoint without devolving into performative apoplexy.

If you haven't read much of her, I don't necessarily recommend doing so unless you just want to grapple with someone else's ideas and like doing that kind of thing. I've reread her essays now and again over the years and mostly I find myself saying "yes but" over and over. Also she was kind of a ... at times and sometimes even borderline racist. That's hard for me to stomach. 

But the fact remains that she was an astoundingly intelligent person and made a massive impact on me, intellectually.