What does Apache provide that other code repositories don't?
People thinking about creating an open source project might rightly consider hosting on one of the various hosting services available: Google Code, SourceForge, kenai, bitbucket and github come to mind. Quick and easy, create a repository or request some resources and you're in business.
Incubating a project at the Apache Software Foundation (ASF) takes a lot more effort than just requesting a hosting space on one of those services, so why would you do that? One can perfectly host code on one of those services with an Apache License, so what's the difference?
I think the big difference lies in the governance model, and in fact calling the ASF just a code repository is very wrong. Let's discuss some key elements of that.
The Apache voting process has been tried and tested since 1999, or even earlier. This is one of the things that projects coming through the incubator have to learn, led by their mentors. Learning is usually very easy as people quickly see the benefits of those simple no-nonsense rules.
The ASF also provides a well-defined structure for managing projects, and the foundation as a whole, in a fair and consensus-driven way. One could argue that structure gets in the way, and sometimes it does, but when things go wrong having a well-defined way of getting back on track helps tremendously. And this structure leaves a lot of freedom to the project's management committee (PMC), there's a lot of room for adapting a project's way of working to its community and goals.
Creating an Apache project is certainly not required for all open source projects (and the foundation couldn't scale to thousands of projects right now anyway), but for the critical infrastructure parts of one's business (what's sometimes called "open core"), having an established governance model makes all the difference.
The governance model is just one of the benefits that Apache projects get - there's also the visibility, brand recognition, nice build services, and other tools, and, last but not least, the many friends that you make along the way! As everybody now knows, there are no jerks at Apache!