I have moved into a home that the previous owners had gotten some sort of crazy glue or rubber cement glue all over. What can I do to remove this without ruining the counter top?

Also, it is on my linoleum floor. Any suggestions for removing it there?
Thank you.

Try using a razor blade on the corian. Any scratches you put in the top can be removed. You can remove scratches by purchasing a corian repair kit.

As for the linoleum, that will be tougher. You can't repair that possible damage.

Hopefully someone else here has an idea for the floor.

Try a product called "OOPS!"

Available at Lowe's. It is an all around adhesive remover. You'll have to put it on a cloth and rub it around on the stuff to be removed. It may take a little elbow grease. But it should work.