Fountains of Bellagio is not only one of the best shows on the strip, but it's completely free for anyone who happens to be passing by to see.
While they do run fountain shows during the day, IMO the best time to see them is at night. While walking past the Bellagio hotel and casino, music can be heard playing through the speakers along the strip, then every 15 minutes you'll see the tips of the fountain heads emerging just above the surface of the water, the music fades out, the lights that illuminate the front of the Bellagio dim, and you're in for a treat!
The fountains and lighting do a coordinated dance and show set to music, everything from fast paced songs like Elvis Presley's "Viva Las Vegas" to Sarah Brightman/Andrea Bocelli singing "Time to say Goodbye" (the best of the Fountains of Bellagio performances IMO).