I have bike tires that read 26 x 1.95. Does that mean I need a 26-inch tube? I ask because my front tire's inner tube got torn and I needed to replace it.

It was 26 x 1.95 as well and I bought a 26 inch bike tube and it was too big -- inflated it would hang 2 inches off the rim and would not fit within the tread/tire part itself, and I am certain it's a 26 inch tire.
Did you inflate the tube off the rim or without a tyre?  they stretch when inflated naked.  

Read the tube side it might be a 27.5 in the wrong box.