A toga party is the one where people dress in a costume that is similar to those of Ancient Romans and Greeks. The name comes from a kind of dress worn by them. Toga is a representation of that culture and this theme is amongst the oldest and most popular amongst party goers.
Some Interesting Activities and Games
Have a setting for a trivia quiz on Greek and Roman mythology including their customs and traditions. Either you can have all the questions put in a hat and have everyone pick from that, with a person in charge of the answers separately. Or another thing you can do is make teams and ask the questions to the teams as a whole.
Certainly enough you would make at least a couple of dishes based on the party theme - something exotic and similar to what they used to eat in ancient Greece and Rome. Blind fold a person, make him or her smell the dish and identify it and list the ingredients. Whoever names the maximum ingredients correctly, wins!
To bring in a unique element, let the guests bob for grapes or olives, rather than apples. martinis would be great for the mix! The first one to get hold of the grapes or olives is the winner! If martini is not possible, just have plain sparkling water in wide mouthed glasses! No hands allowed, only mouth can be used to get the grapes or olives. Have a time limit to make it even more interesting.
Be it poetry or any kind of a dramatic performance, it comes out the best during parties. Thus, have a poetry recital. Trust me it can be absolutely hilarious. Have the guests write something on the spot related to the theme and recite. It will be amazing entertainment!
Although, if you want, you just need to give it a little thought and improvise and innovate. You can come up with better games!