[goodcanadian]

Yes, they will. The only place you can put a geostationary satellite is on the equator. In theory, they stay in position above the selected point on the equator. In practice, they aren't perfectly stationary, and they will move around the designated point, which will, of necessity, cross the equator.

[mdszy]

for the practical purposes outlined in the context of this thread, they do not cross the equator

[iguy]

For the purpose of Africa vs Europe, they can't really be positioned to have a better view of Europe than of Africa.