We have a cinderblock foundation to our home (built 1940) and in renovating one of the basement rooms, we found a 3/4" galvenized water pipe with an in-line valve, then a hose bib coming off of the valve, sticking out of the cinder block (about 4" above grade as half of the basement is exposed). Of course this monstrosity is sticking out into our intended walking space by about 8 inches. We were going to try to take off the in-line and cap the thing (reducing its intrusion to 4 inches) but the valve WILL NOT come off (PB Blaster, Knock-er-loose, blow torch, nothing will get this thing off). We opened all the valves on the pipe, and no water comes out (we initially got some air, but that's all). The water main is on a complete opposite corner of the house. Any idea what this pipe is/is it safe to just cut it off and leave it uncapped?

I haven't a clue what a old 60 year old pipe went to but I know what I'd do with it. Block walls right? And you're going to fur out the walls and drywall and paint, Correct? And you know this is a dead line, right?
Then I'd cut that 3/4 tight to the wall and drywall over it.
Worried about leaving a open line in the wall? No problem! Make your cut a inch or so close to the wall. Get a set of 3/4" pipe dyes and put a threade on the pipe and cap it off. You'll have to fur out a little farther but your pipe will be hidden. Since the pipe's been setting there open without any floods I'd simply cut it short and wall it in. Good luck, Tom

Could be an old well line or an old city supply that corroded out. As Speedball says, cut it off, maybe fill it with Bondo or hammer a wooden dowel in it and cover it up.