How fast do we travel through space?
According to the Astronomical Society of the Pacific's website "How Fast Are You Moving When You Are Sitting Still?", we are moving:

Rotation of the Earth: 1600 km/h

Orbital rotation of the Earth around the sun: 107,000 km/h

The sun around the centre of the galaxy: 792,000 km/h

Going further, according to the article "Milky Way Galaxy: Facts About Our Galactic Home" (Redd, 2013) quotes the sun's speed around the centre of the galaxy as 828,000 km/h

The Andromeda Galaxy and the Milky Way are headed for a collision at 112 km/sec

According to "Milky Way moving away from void" (2007), the Milky Way galaxy is moving from the local void at 600,000 mph (960,000km/h)

According to the article "The Universe is expanding at 74.2 km/sec/Mpc" (Plait, 2009), the Universe is expanding at a rate of 74.2km/sec per megaparsec (3.26 million light years).

There seems to be some divergence of values in the articles, but these give a good estimate.