1) You don't pay rent. Once you own the place free and clear, it's yours and you always have a home.
2) While the house depreciates, property may may still appreciate, especially if you live in a nice area, and even more so if you own the land beneath you.
3) There are tax benefits to owning your own house.
4) When you start out, it's usually not that much wealth, since you're taking a loan on it, though it is highly leveraged. As you pay more of it down, if you're smart, you'll have diversified your assets, so it's not all in one spot.