Question

Spanish speakers sometimes shake hands to greet each other or to say goodbye.

Answer 1

Well, not really. They do the "beso" or cheek to cheek kiss.

For goodbyes, the "beso" is usually accompanied by the "abrazo" or hug.

That's how they do it here in Spain

Answer 2

For Spanish speakers here on the border of Mexico and Texas. We usually shake hands to greet each other or to say farewell. It all depends on the relationship that the Spanish speaking people have with the person they are associating with.