I'm a REI novice but CC hacking master :-) I like getting the rewards and benefits. In fact, I plan on using CC as much as I can when buying things for real estate. However, I'm good and never carry a balance. Also I am active duty military so I take advantage of the tons of benefits companies offer (low interest from 0-4% and no annual fees, even on my Amex Platinum!)
The benefits they offer are great - from return protection, extended warranties, to car rental insurance. If I can, I always put it on a credit card. To answer your question, I probably have 10 or so credit cards. For your average REI, 2-3 are probably good. One each that gets you great points/cash back/miles at office supply, home improvement, and gas stations. If you find yourself traveling a lot, a good airline CC can get you some free trips to check in on your properties too!
Edit: I should add that types of credit matter a lot. Because I don't have a mortgage, it'd be "harder" to get a mortgage (non-revolving) even though I have 50K+ in credit available for credit cards (revolving type credit). So having good credit with cards will probably help but you need mortgage history to really bump your score. Also spreading debt over cards and not using more than 30% of any card shows good history as well. Credit card inquiries ding your report, but they're usually only on there for a quarter.