I'm using Litespeed (the free version) for some months now.
I started with one subdomain and converted my whole site over to it in some weeks, trying to put more and more load on it (currently serving 30-50 req/s).
Before I was using a combination of apache (for dynamic php-content) and lighttpd for static files.
While converting I stumbled across some problems (mostly related to port some feature from my previous configuration to litespeed) but those there fixed right along, often already in some hours.
Even new features are implemented very fast after just asking for them .
Over apache I liked the way to have just single process which is a high-performance-webserver for static contents and can also do php through fastcgi (which keeps the php-processes out of the webserver process -> more stable webserver) with at least the same speed as apache (I see roughly some 10-20% more req/s on my php-apps).
Another great thing is their webinterface to control every aspect of the webserver. You can add ips, vhosts, fcgi-apps or whatever setting you want to change in the controlpanel. You don't need ssh-access to just control your webserver. I case of a crash or something like that (I had just three of them and all were fixed right after reporting them) the supervisor-process restarts the webserver -process.
Oh and, different from the other alternative webservers, they support .htaccess files from apache without changes, full mod_rewrite support (all my older rules worked!).
If you need some special apache-modules you will need to stay with it but otherwise I would just try it out .
What you could see as "bad" is that its a relatively new webserver which might have problems and that its closed source and the free version is limited to 300 concurrent connections (I don't need more right now), but I think its worth it.
I've been testing LiteSpeed Enterprise edition for the last few weeks and I have to say that I'm very impressed with its performance and rich feature set. The documentation is quite complete and moreover the email support is also very good. George has been very patient, polite, responsive and helpful with me and we've been exchanging a few dozens of emails.
Installation (and upgrading) is quite easy and straight forward. When I installed it in the second box, it took only less than 15 mins to install and configure everything and go live with litespeed. They said they are developing a better integration with Apache and once it's finished it will be able to import Apache configuration transparently and being a perfect replacement for Apache which can be used in any control panel. In the meantime, I don't think you can just use litespeed along with DirectAdmin or any other control panel easily to manage many domains/vhosts.
Being commercially supported (with a reasonable pricing), I think litespeed has a great future and can be considered a high end webserver comparable to Zeus.