It's not about the Apache web server, and I know there are a lot of actively maintained and respected projects under the Apache label (Lucene, Tomcat, Maven, ...).

I think the project that gave the most sour association was OpenOffice, which was donated to Apache when it was already over and the LibreOffice fork was well underway, and it has been on life support ever since. I recall there were a couple other projects with a similar fate but to be honest it is probably more of a brand reputation thing than an assessment of the quality of every project.