I've been running Apache HTTPD for seven years and it hasn't let me down yet. I am continually impressed at how configurable and stable it is. This goes without saying, as it is the de facto standard.
Being a sys-admin and web-developer I have a profound respect for this beautiful project.
I've experienced uptimes of over 7 years with Apache based servers - and never had a problem I haven't caused.
The Apache HTTP Server is arguably at the top of its class - Thank you.
Apache is the industry standard. As such it commands a high degree of respect. The biggest asset that apache has is that you can trust it. You can trust that development isn't going to stop tomorrow. You can trust that it's still going to be around in a few years. You know that you can get support. You don't have to worry about the software being abandoned a few weeks after completing a project that depends on on.
For some these are very important reasons to pick apache. On the other had there are several newer http servers out there that are less bloated, quicker on their feet, and still provide all the features most users will want. So if you want a server that you can depend upon not only from a technical perspective but also from a social perspective, apache may be exactly what you need, but if what you want is something a little lighter and easier to completely wrap your head around then projects such as lighttpd or nginx might be worth a look.
I've been using apache for years. I've also used many different web servers. (I'm a little obsessed with trying out new software.) Apache is by far the best, fastest, most configurable web server I have ever used. If you need it to do something it doesn't already do, just go ahead and write a module for it.