It depends on your goals. For instance if you like to trade stocks short term as well as keep a long term portfolio it is sometimes advantageous to use different brokers as their fee structures are so different. That being said, for most people as long as they're under the insured limits keeping money in only a couple different institutions is fine.
I tend not to chase rates that often or take advantage of opening offers and then closing accounts as I really don't think it's worth the time or trouble. Some people are really good at this kind of thing but I've spent the last year trying to simplify and consolidate my finances and am much less stressed with that approach.