As announced at the WWDC 2009, Apple is starting to offer the new iPhone 3.0 Software update for download today June 17th.
The new iPhone OS available for free for current iPhone users is offering over 100 new Features. iPod touch users have to again pay $9.99 for the new iPhone Software Update.
If you ordered the new iPhone 3G S you do not have to worry about upgrading and you get to use more of the new iPhone 3.0 OS features including, Video recording, Voice Control and Digital compass.

Apple already prepared the download pages for the new iPhone Software Update, but as of writing this story the downloads are not available yet.
Update:
Looks like the iPhone 3.0 OS will be released not in the morning as some overseas Apple pages (e.g. Singapore) say that the iPhone 3.0 OS will be released June 18th (Via Engadget).

Update:
User gjking2001 posted below that Apple will release the new iPhone Software Update at noon PST.

Update:
iPhone 3.0 Software Update available now!

iPhone 3.0 Software Update for iPhone page
iPhone 3.0 Software Update for iPod touch page.