I prefer playing face to face. But sometimes it's not possible. Or you want to play in a campaign where your GM is in Pennsylvania, and you live in Oregon. Google Hangouts is simple. Players have their printed character sheets, a computer, video and audio, and off you go.
Edit June 29th, 2017: Dice Stream doesn't work on Google Hangouts anymore, because Google dropped all support for the Hangouts API. :( You'll need to roll dice by hand or use a second window with a dice rolling app. I use https://rolz.org/.
I'm talking Google Hangouts with the DiceStream App. This is one of my favorite ways to play online. You see everyone's smiling faces, and whoever is talking gets their video feed plastered on the big screen, while everyone else is down in little windows at the bottom. It's almost like being together, though you can't share drinks and snacks.
The GM can switch windows to show maps and other handouts. Use the green Screenshare button on the left side of hangout.
Running a game over Hangouts with DiceStream works well for theater of the mind type games, where you run without minis and just describe everything. DiceStream is perfect for games with fairly simple dice rolling mechanics. For example, Numenera, Trail of Cthulhu, Fate Accelerated, or Basic Roleplaying all work well in this setup.
Click on the Dice Stream icon on the left of the Hangout and start rolling dice. If you roll the same numbers of dice often, I like to go into Dice Stream's Settings tab and uncheck Clear Dice Selection After Roll. I usually check Clear Dice Before New Roll, so my screen doesn't get filled up with old dice rolls.
You can add the Hangout to a Google Calendar event, which will send reminders to your players.
Google Hangouts is free and can be found here -> https://tools.google.com/dlpage/hangoutplugin/
DiceStream is also free and can be found here -> https://plus.google.com/107354344238067073375/about
Click on the Start a Hangout with Dicestream link. From now on, you'll have DiceStream in Hangouts.
Here's how to create a Hangout for your game in a Google Calendar event -> https://support.google.com/calendar/answer/2690797?hl=en
Here's a great Tutorial Video from Starwalker Studios -> https://youtu.be/AcGXJVrjml0?list=PLUGTtv2RH-6G-mc55STfzEh06y1uD6NVR
Next I'll talk about using the Roll20 virtual tabletop. This is great when you want more powerful dice rolling and/or a virtual tabletop.
And don't miss -> Getting Started with Fantasy Grounds