Apache return 304"s, refusing to update pages

I've changed a file, but when I browse to it, it doesn't change. I've
also deleted it, copied other files over it, etc. Doesn't help. This
has occurred with a .php file as well as a .png. In fact, the .png is
sitting inside a directory that doesn't even exist anymore.

The access log shows that Apache is giving 304's, which I guess means
it's sending information from the cache. But why doesn't it notice
when I change things?

I'm running Apache 2.2.3 on Redhat EL4. The problem occurs with
Firefox or IE.

Also of interest, when I created a new file in the same directory,
Apache served it nicely, and when I changed it and did a browser
reload, I got the changed file.

I've seen various reports on the web (from at least as far back as
2002), but I can't tell how many separate problems it is, and what the
solution is. I believe I could run htcacheclean, but I'm worried the
problem will come back every time we edit our files.

Help!?

-Amir Karger