In the past I never took the time to watch this -- shame on me! And you really can't go wrong with this!
Free and fun to watch with the accompanying song playing on the speakers at the same time. A large crowd can gather, so shuffle in to find a spot at the Bellagio walkway and if you don't make it at the right time, guarantee you will catch another show very soon! They run frequently, roughly every 15 minutes. Even just walking on the strip and passing by, it's fun to glimpse at, especially at night time. To really enjoy it, take a moment, stop and stare!
Once you're done with that show, check out the street performers. One that caught my attention was a ballerina. It was freezing but she was a great dancer nonetheless!
There are also amazing views of this shows from the top of surrounding hotels. I personally think it's better on the ground level, so you can really see the water shooting up into the night sky.
Would be cool if they did special/holiday themed lighting, but then I think that might ruin the classic vibe/tradition of the Bellagio fountains.
So enjoy!