If you pay for any improvements to the property, you can depreciate them, too. It may look like one building to you, but to the IRS it could be multiple depreciation accounts. Congress is constantly changing the depreciation rules and periods. It can be a mess. But it's worth it.
Real estate is a high-maintenance investment.
You can't stick it into a safe deposit box and just collect dividends. Depreciation is part of the payback for all the hard work that may be involved. Let's say you live on the property. Let's say you live in one unit of a multi-unit apartment building. You can't depreciate the part you live in.