Virtual conferencing is serious technology, for serious people and serious businesses. That's why it may take a little effort to make it fun and relaxing! Just like in a physical meeting, there is a period at the beginning of a virtual conference where people tend to be unsure or uptight. To get past this point and down to a more productive meeting, you might need to break the ice.
(A word of caution: these suggestions are best for more relaxed situations and care should be taken in deciding which situations are appropriate for use.)
To break the ice on a conference call, distribute a famous Sean Connery line or mini-speech to all participants beforehand. Then, at the beginning of the call, have each person say the line in their best Sean Connery voice and vote on who does the best impersonation. (You may pick a different famous person if you like.)
Another idea is to distribute sentence fragments along with a number that represents where the fragment is in a paragraph. You can start off by reading your fragment, and then everyone must chime in with theirs at the appropriate time. There will be sure to be some hilarious mistakes, especially if you choose a good paragraph. See how fast you all can get through it!
Never forget the power of a joke. Have everyone come to the conference call with a short joke. Let them all tell it in turn and vote on the best one. (Since there is always that one person, make sure to tell everyone to keep it clean and appropriate.)
A video conference could use all of the suggestions above, but you're neglecting the great potential you have in being able to see everyone. Have a pirate themed video conference! Tell everyone to dress up in pirate garb and see how long you can get into the meeting before too much laughter dictates the removal of costumes.
Start off with video conference charades! There's nothing fancy here, just do the game as you normally would and try to ignore the fact that all of you are far apart.
A good rule of thumb: if you treat virtual conferences like physical conferences – in etiquette, meeting mechanics, and even ice breakers – you'll find that they will run smoother and be more successful.