I'm a HUGE fan of REITs...but they are difficult to "back test". The Great Recession was fueled by exotic real estate backed debt, so REITs actually suffered worse than stocks for an asset class that's supposed to be more stable. I hate to put it like this, but you almost have to toss history out the window.
I'm not a fan of indexing REITs, as someone mentioned, it's like Bershire Hathaway, you're already paying a management team to own 100s of properties, pick the REIT. Some REIT indexes also include mortgage REITs, which are often just high risk lenders. The asset class has a huge spectrum of risk/return, each of which you'll get a different yield from.
I personally own two:
STAG Industrial: To me this is about as safe as they come, 300+ industrial buildings, primarily distribution centers setup along interstates with major companies as tenants. No concentration risks in either markets or tenants. These properties tend to hold their value or go up and they get nice increases. Yields in the low 6%s
Entertainment Properties Trust: This is higher up the risk/return spectrum, focusing on more specialized properties difficult to get bank financing on, such as movie theatres, recreational complexes (Ski Resorts, Top Golf), and childhood education / charter school facilities. I've owned this thing on and off for 15 years, one of my biggest investment mistakes of my life was not going 100% into this company in the depths of the recession and quadrupled my money. The movie business is one of the few businesses that improves when times are bad... Yields close to 8% right now, currently at a nice discount because the market got scared about movies last year and they've got an issue with 2-3% of their revenue on a big daycare tenant.
Do your own research, but those are my holdings.