Pride of Ownership - It is a great feeling to own your own home. This benefit may be enough to outweigh any disadvantage previously listed. With your own home, you feel a sense of stability and community that you probably didn't feel when you rented. This comes from the fact that you own a piece of property in a neighborhood along with others enjoying the same benefits as you.
Investment - Since you are going to have a housing expense for most of your life, it is definitely worthwhile to consider investing some of that expense in a home of your own. For those people who plan on staying in a home long enough to pay off their mortgage, owning a home is a forced savings plan.

Appreciation - If your house increases in value (becomes worth more than you paid for it) you will benefit from this appreciation. As you continue to pay your mortgage, and your home appreciates, your equity grows. When you sell your home, this equity will become dollars in your bank account. It is important to carefully choose your home so that over time you will benefit from appreciation, because it is not necessarily guaranteed.

Tax Savings - Consult your tax advisor for the specifics of any tax savings you might benefit from with owning you own home. Usually, some expenses may be tax deductible such as mortgage interest and property taxes.
These are just some of the benefits.