Having said that, I'm looking at Varnish (once the stampede dies down) ...
If you switch to nginx, then you probably won't need varnish at all and can replace Apache.
The nginx config is much, much, much easier to work with than Apache. Transferring complex rewrite rules is the hardest thing to get right when moving over, but everything else is much easier.
Smart lobsters use nginx
* Changing Apache would have required changing other packages - PHP wasn't thread-safe.
* Varnish looked fragile. I wish I still had my notes about why I thought that.
* Nginx in front of Apache was relatively quick to setup & really great in practice - restarting an order of magnitude less often.
If the nginx config file would be useful as a starting point, I offer it.
Edit: formatting.
I'm not sure if it would help me, but I'm almost certain it would help other people - so please, consider your offer accepted if you can find somewhere easy to publish this :)
(Compression & other varying content was a headache - separately caching & serving gzip, deflate, & unpacked versions, without any built-in compression.)
Those tweaks looked time-consuming to set up, hard to test, & liable to break quietly. A buffer in the way that simply & quickly gets a response from (& then frees up) Apache, then slowly feeds the response to the client, provides most of the benefit; nginx fills this role well for me.
Other than that Apache is pretty much king with compatibility and nginx is pretty hard to get to similar qualities off the bat.
But if you have the space something like a reverse proxy for Apache with sane times set would probably be the better option.
I use cherokee on VPS's though and it works great.
Cherokee is a possible alternative too; that has some default configs for Wordpress etc. that work well. But for anything custom I found it a nightmare to get "just so".
Nginx is a neat alternative to Varnish as well; for example I'm having great success sitting it in front of a Cherokee site (serving the http) to provide SSL :)
http://www.coldhardcode.com/2009/04/varnish-and-movabletype-...
The same is true for wordpress:
Nginx is great, for example, but the docs are primitive compared to those for Apache, which has been around forever and which has spawned thousands of hints and snippets all over the web.
EDIT: At this point I should probably say out loud that for accelerating static pages it might well be simpler to get a reverse proxy, e.g. Varnish, running in front of Apache than to actually ditch Apache.