Before you think about launching a site, make sure you have your bases covered! Here are the top three things I always have on my "checklist".
There are a couple of websites I'd recommend for doing this:
Adobe BrowserLab is another super cool screenshot service with a really nice interface (what do you expect, it's Adobe) and handy features like viewing screenshots from what they call "browser sets" side by side and overlaying screenshots on top of each other. There are lots more features that I'm too lazy to put in this post, but you can view them here! I don't think it's free, but I was able to sign up for a complimentary one year subscription.
If you'd like to actually like to test out your application, you might consider using CrossBrowserTesting (aptly named), which allows you to remote into their testing machines and actually try out your application in a bunch of different browsers and operating systems. I've never actually tried them before, but I've heard good things about the service. It's a little pricey, around $20 a month for 150 minutes of testing time a month.
Pro Tip: don't accidentally leave your session with them open on your browser.
If you're like me, aka you take great pleasure in looking in all the page view statistics on all of your websites, you'll love having analytics installed. Make sure you install analytics BEFORE your launch, or you'll be sorry you missed out on the exciting graphs (I deeply regretted forgetting to install analytics on REOrganize before I launched).
If you're launching a web application (vs. a static page), it's essential that you have exception notification. Standard exception notification services will email you if any exception is raised in your application along with a log/stack trace, and may even offer premium features. You can usually find plugins for whatever app framework you're using - for example, Rails has an exception notification plugin you can install that uses your server's mailer.
(Update: I've written a post on how to use exception_notification here)
If you don't want to worry about installing anything, you can go for one of the many web services out there. I've used HopToad before, which offers a free "Egg" plan for one application and comes packaged with a gem you can easily install in a Rails application. Exceptional is quite good as well, but only for Rails (I basically only know about Rails services, if you haven't noticed already).
These are the top things that I'd recommend that most people never think to do before launching a website; maybe I'll mention some smaller (but still important!) things to check for in a future post.
PS: Merry Christmas/Happy Holidays!