If you're standing at the water's edge, the horizon is about 3 miles away. If you click
here, that will link you to a web-page which has a handy computer version that helps you work it out. All you do is put the height of your eye relative to the water's edge into the slot and click on 'Compute'. So, if you're eyes are 5 ft 6 inches above the ground - ie 5.5 ft - put that into the slot. If you are standing on a 100 ft cliff, put 105.5 in.
As for looking into space, you can obviously see as far as the furthest-visible star/galaxy...ie multi billions of miles away!