RedHat Linux versions 4.x (and possibly earlier) RPMs contain various nasty scripts which do not stop or restart Apache properly. These can affect you even if you're not running the RedHat supplied RPMs.
If you're using the default install then you're probably running Apache 1.1.3, which is outdated. From RedHat's ftp site you can pick up a more recent RPM for Apache 1.2.x. This will solve one of the problems.
If you're using a custom built Apache rather than the RedHat RPMs then you should
rpm -e apache. In particular you want the mildly broken
/etc/logrotate.d/apache script to be removed, and you want the broken
httpd.init) script to be removed. The latter is actually fixed by the apache-1.2.5 RPMs but if you're building your own Apache then you probably don't want the RedHat files.
We can't stress enough how important it is for folks, especially vendors to follow the stopping Apache directions given in our documentation. In RedHat's defense, the broken scripts were necessary with Apache 1.1.x because the Linux support in 1.1.x was very poor, and there were various race conditions on all platforms. None of this should be necessary with Apache 1.2 and later.