Essentially every Dreamcast game feels like a "vacation" from games on all other systems.
Running through Emerald Coast in Sonic Adventure.
Doing solo flights in AeroWings.
Watching highlights of the fares you drop off in Crazy taxi.
Watching your airship duke it out with another one or a giant monster in Skies of Arcadia.
Watching your favorite Soul Calibur character in "attract mode".
Playing the sci-fi action/adventure cinema-like Blue Stinger.
Replaying the races you did in Speed Devils.
Listening to the oft-ambient, soothing classical space music in Armada, while zipping around the galaxy, and asplodin' the enemiez.
Getting a slice of life in Yokosuka, Japan with Shenmue.
The list could go on and on!