When we moved into our home 17 years ago, the finished basement is what sold us. It's one open room, with a bathroom off of it. What I love about it: it has shelving built in, surrounding entire room, love this for storage, place framed pictures on etc. One side of room is a sectional couch with tv flat on wall, strongly encourage this, especially if you have growing children, as my kids got into their teens it was a fantastic place for their friends to come and hang out on. The other side, is a ping pong table. Again, fantastic fun for teens. Other things I love, lots of windows! Basements are dark, so have lots and lots of lighting down there. And definitely if you can swing it, a bathroom is a must. Love our finished basement!
This pretty much describes ours, too. Our laundry is part of the bathroom, which works out fine. We also have a large storage room which we recently renovated and re-organized. We have a second fridge in there as well as the dog food, extra pots and pans, cleaning and other household supplies, coolers, etc. I love having that room.
We've done it once already, but are about to re-renovate the whole family room, and I can't wait. We added built in bookcases on both ends of the room, at the far ends. Those are great for storing DVDs and games, books, pictures and mementos, etc.
The large screen TV is still on a corner stand now, since pre flat-screen days, but will be going up on the wall soon, which will cause us to re-think the furniture arrangement. Ours is almost like two rooms even though it's one big one. One side is the TV area and as others have said, it's a teen room now with gaming and dance parties, etc. The other side has our desk and functions as a home office but there's still room left over. We have a futon there now, for extra seating and sleeping for sleepovers. This might make the cut list since I have a sleeper sofa now, although it does come in handy for storms and such if we all have to stay in one room. Even though our kids will be in college in a few years, I imagine we'll be having granchildren using this space someday.
On my wish list for this space is a wet bar (which I don't think will happen for us now because we have the other fridge a few steps away where cold drinks are available, but it would haver been nice over the years while our kids were growing up and the house was really busy to have a wet bar with small dishwasher and glass and plate storage, etc.) and perhaps a pub table because realistically, we and the kids often eat down there when we're watching a movie or hanging out, etc. (Although our main adult TV area now is in our new sunroom.) If we don't do a pub table, I would love to put some type of game table there that the kids could enjoy, like a bumper pool table or air hockey. I wish we'd done this earlier, but we always had so many other renovations, this kind of took a back seat since we'd already done it once when the kids were little. It would come in handy during the long winters and give the kids something else to do besides electronics (and outdoor stuff). We actually did have a combination game table there on top of another table, but we should have sprung for a good one. I'll probably still do it if I can find something after we renovate. I'd probably even do this over a pub table, since we have a large, square coffee table in the TV area which functions pretty well as a table, albeit a short one.
We don't get water persay, but it can get damp in the summer unless we run a dehumidifier. When we renovate this time I think we will not do carpet for that reason. Even if it's clean, it can get a mildewey smell which requires cleaning.
Another thing I would have liked to have is an area for extra clothing storage. We don't have room in this space, but we have a real cellar, under our in law apt, where we're in the process of building a cedar closet mainly for coats and boots, which take up so much space in regular closets. Some people here have described areas under their stairs for closets, which would be great. I would love that but it's not possible where we are as the stairs have full walls next to them. If you live in a large house with lots of closet space, it's probably not an issue. But in an older house with limited closet space, it's really needed for an active family.
Good luck with your basement!