Hmm, I think "too many" is when you can't track all of them on a regular basis and you get hit with inactivity fees.
Just like credit, there are different reasons for each one of us for different deposit accounts.
And then some people like to "ladder CDs." Software helps. Then there are people like my mom who track without software (she introduced me to "laddering" when I was in HS!).
About 6 years ago, I took major advantage of checking, savings and brokerage account bonus promos for opening. When I became pregnant, I started consolidating and closing accounts because there was no way I could keep them all open and avoid fees. Now, we're on a tighter budget so I've been opening deposit accounts again to get bonus money for the holidays. Many T&C require accounts must be kept open for 90 days-6 months. And it looks like I'll be keeping most of my new accounts, I stumbled across one bank that rebates ATM fees and I like Chase's online banking. I also like the 3.45% no min bal checking account I have at ING.
To add diversity, I just added a credit union (I do already have one from work though).
Downside, I've been getting hit with hard inqs for just about each new deposit account.