Pro Great for shared hosting and smaller projects
Since Apache doesn't handle a large number of concurrent connections like Nginx does, it's better suited for smaller projects. Apache's .htaccess file (which overrides system-wide settings on a per directory basis) makes it a great option for a shared hosting configuration as well.
Pro Mature server with a mature userbase means you'll get good help
Apache has been around for a very long time and currently 46.2% of the web uses it. Because of its maturity, you can hop onto any old forum and generally expect your question to be answered. Notably, sites like Wikia, Paypal, Senate.gov, and Forbes all use Apache.
Pro Includes a wide array of modules
Apache comes packed with a bundle of modules that provide differing functionality. Some notable ones are mod_lua, which provides lua hooks into portions of the httpd request, and mod_ssl, which provides strong cryptography using the SSL and TLS protocols.
You can see a full list of modules here.
Pro Easily configurable with three different multi-processing modules for different server loads
Apache is configurable in three modes: Process model, worker model, or event model. Process is the original "pre-fork" method. It's good for smaller sites, but has trouble with concurrent connections and may even deny requests at higher load. Worker creates a single control process that generates child processes, which in turn create a fixed number of threads which listen for connections and pass them back up the chain. It scales better than the Process model, but large sites can still see bottlenecks. The Event model is similar to the Worker model, except instead of creating child processes with listening threads, it creates one listening thread which passes requests to a worker thread. The Event model handles long running connections the best and is the default configuration for Apache.