We use Selenium Core, but are switching gradually to Selenium RC which is much nicer and easier to manage. We have written lots of custom code to make the tests run on our Continuous Integration servers, some of them in parallel suites to run faster.
One thing you'll find is that Selenium seems to restart the browser for each test (you can set it not to do this, but we got memory problems when we did that). This can be slow in Firefox, but is not too bad in IE (one time I'm thankful for Bill Gates's OS integraion).
