I just pulled up the floor in my living room and found an open pipe in the ground. It's white pvc and is almost full of water. I tried sucking out the water with a Shop Vac, but it filled right back up. I'm thinking it's some kind of drain pipe. Is it safe to plug this pipe up and fill it with concrete? I don't want a pipe full of nasty water under my living room floor!

You do nothing until you find out where it comes from, and it's purpose for being there FIRST. Sounds like a drain line, but from what and where, is the question to answer.

I just pulled up the floor in my living room and found an open pipe in the ground. It's white pvc and is almost full of water. I tried sucking out the water with a Shop Vac, but it filled right back up. I'm thinking it's some kind of drain pipe. Is it safe to plug this pipe up and fill it with concrete? I don't want a pipe full of nasty water under my living room floor!
That pipe goes somewhere, and that water is coming from somewhere. You DO NOT want to plug it up, you WILL have created a very expensive problem to fix dumping concrete into it... now capping it isn't a problem as the water is left free to go where it needs to. But I would not GLUE a cap on, you would want something what can be removed if needed.

Does it overflow ? Is ground wet around the end of the pipe ? Where does it go ? Can you see if it goes to the outside or to the basement, etc ? What is approximate diameter of the pipe ?

I would monitor it for few days to see it starts overflowing. It can be left over pipe from when somebody added onto the house and left existing yard drain cut off and opened under the house

Back to you

Milo