Men and Women Cannot Be Friends
The entire movie is based around Harry's deeply ingrained belief that men and women cannot be friends because sex always gets in the way. There is always a little bit of a spark between Harry and Sally but it seems to be based more upon light bickering than anything else. Despite Harry's belief he finds himself with a female best friend in Sally. They do all of the things that a couple dating might do - lunches, museums, art exhibits - but they never date. They also act as each other's New Year's Eve date when they are not involved in relationships, and go out on double dates when they are. They set up each other with their friends (although this doesn't go entirely as planned when their friends hit it off and end up marrying each other) Then one evening when Sally is upset over a break up, they have sex.
The friendship changes. Harry's contention that sex gets in the way of platonic friendship actually turns out to be correct. Once he and Sally have slept together their friendship becomes awkward and strained; the are distant and things just aren't the same anymore. Even though they ultimately realize that they love each other, and they subsequently get married, this still continues to prove his point; after sex, the friendship is forever changed, and they cannot be just friends anymore.
Romance
This is a romantic comedy and so one of the key themes is romance. Harry and Sally are not a romantic couple, at least not at the start of the film, but we do see them with their respective partners albeit during the downhill part of their relationships. The "friendship" dates that Sally and Harry have are actually quite romantic but always occur when they are dating other people.
We also see the romance theme in the way in which their best friends fall for each other; it's clear that the path of romance already has its own ideas, because although Harry was intending his best friend to fall for Sally, and she was intending her best friend to fall for him, the heart wants what it wants and they are instantly smitten with each other. The film also has a very romantic ending as Harry tells Sally all of the things he loves about her and why he is in love with her.
