This is Rick’s strategy that I’ve adopted.  It works well for me, and has for him over the past decade.

    Apply for no more than one card from each of the card issuers (American Express, Bank of America, Barclays, Chase, Citi, etc) per 91 days.  If you decide to add business cards as well, then one personal and one business card from each issuer.  Why wait 91 days between credit card applications?
    Each inquiry will decrease your credit score 2-5 points, and will completely fall off your report in two years.  If your credit file is thin (younger / less accounts) you’ll notice a larger hit to your score.  Also, keep in mind that most (but not all) applications will only query one of the three major bureaus, you want to track where the inquiries are going (your credit report will tell you) as you may notice one score continually being hit while others not.
    All of your credit scores should stay over 700 (on the FICO scale) at all times and if they fall below that number STOP until they recover.  Scores over 700 are considered very good to excellent.  We want to only use your excess credit here; in the event that you need a loan of some form we want to make sure you’ll still be approved for it and at favorable interest rates.  Looking for car / home loan … keep those FICO scores safely over 740.
    Try to never let your current balance exceed 50% of your credit line on any given card.  Pay them down before the statement closes if you end up temporarily over 50%.  Have a card with a $5000 limit and make a $3000 charge?  When you get home, send in an early payment of $1000.  While creditors will issue large credit lines, they don’t like them to be highly utilized … especially if you’re looking for additional / new credit.
    Make sure you can easily meet the minimum spend on multiple cards.  It will influence the cards you apply for.  Don’t take on more minimum spend than you can comfortable do within the given time frame.

With a foundation of the above, below are some of the guidelines to work within.  If needed you can always contact the banks for application information.
American Express

    A card account must be closed for 12 months for you to apply for the same product and be considered a new customer
    Cannot open a similar card product if you’ve had one within past 90 days (e.g. Delta Gold Personal when you’ve had a Delta Platinum Personal) … nothing wrong with getting a business version though :)
    Leverage the variety of business cards to help maximize bonuses

Chase

    Applications no closer than 30 days apart (There have been scattered reports of well established Chase customers receiving more than one personal card within that 30 day period.)
    Must have an account closed for 2 years to be considered a new customer of that card

Citi

    2-browser method useful for AA cards
    Expect 18 months between card applications to be considered a new customer
    If you don’t get instant approval, call same day the reconsideration line (800-763-9795) and offer to move credit line

** It appears to me that the two easiest issuers to get repeated signup bonuses with still open cards are Bank of America and Barclays.  I’ll keep them to 6 months a piece and will leave any FF account numbers of the application to make this easier.