Thanks for the link Canuck, there was some useful info there for me. It seems the main reason people add them is that they have a varying correlation to stocks and bonds, which I can understand. But it still seems a little dirty to me for an index investor to go overweight in REITs just for this reason (don't I want all the assets in exactly their percentage of the market?). That link shows REITs making up anywhere from 0 to 2.5% of some of the standard big indexes. Is there something going on here where real estate actually makes up more of the economy than its representation in the stock market? That seems like the only way I could convince myself to add it...
Correlation - they don't behave like normal stocks.
They aren't valued like normal stocks - you look at FFO, funds from operations, rather than p/e. Also there are different regulations - they have to give back a percentage of their free cash flow or somesuch (look into that one, country dependent).
Remember "the goal" isn't to perfectly track "the" market. It's to make money. The easiest way is to track the whole market, sure - but if adding some REITs to smooth out the bumps/give income/whatever fits with your preferred asset alloc, and you will rebalance to it, it's fine.
A whole market (which market? One fund doing the world would be great... but do you want more emerging? Bonds?) fund is what is said because it's likely to produce the greatest return, going from history. Real estate tends to match inflation over time.
So.. no compelling generic reason to buy REITs, but likely no harm in having 5% VNQ.