Amex has a rule of 5 credit cards at any given time and allows for 1 card every 5 days and 2 cards every 90 days. This does not include charge cards such as the Amex Gold or Platinum.
Chase has a rule known as the 5/24. This means no more than 5 credit cards opened every 24 months and 2 credit cards every 30 days.
Chase will not approve you for additional cards if you have opened more than 5 cards in the last 24 months. This applies to all of your credit cards from any bank, not only cards issued by Chase.
Bank of America has a rule known as 2/3/4. This means 2 cards every 2 months, 3 cards every 12 months and 4 cards every 24 months.
Bank of America also has a 7/12 rule which means they will not approve you for an additional card if it's going to result in you having more than seven cards opened in a 12 month period.
Capital One has a rule of 2 personal cards at any given time and 1 card every 6 months.
Citi has a rule of 1 personal card every 8 days and 2 every 65 days.
US Bank requires you to have a prior relationship with them to get their Altitude Reserve. One can open a checking account with them.
Dining - Citi Custom Cash (5%), Amex Gold (4%)
Grocery - Blue Cash Preferred (6%), Amex Gold (4%)
Gas - Blue Cash Preferred (3%), Citi Premier (3%)
Airline - Amex Platinum (5%), US Bank Altitude Reserve (4.5%)
Streaming - Blue Cash Preferred (6%)
Transit - US Bank Altitude Reserve (4.5%)
Hotels - US Bank Altitude Reserve (4.5%)
Chase Ultimate Rewards gives 12.5% off on Hotels, Car Rentals and Dining and 6.25% off on Travel when booked through their portal.
These credit cards have no annual fee, rewards, credit score requirements or welcome bonus.
These credit cards have no annual fee. They do offer rewards in terms of cash back and or welcome bonuses of up to $200. They generally have a credit score requirement of 600.
These credit cards have annual fees of at least $95 and up to $300. They do offer rewards in terms of points, nights at hotels and welcome bonuses of $500. They generally have a credit score requirement of 700.
These credit cards have annual fees of at least $450. They do offer rewards in terms of airport lounge access, top hotel status as well as various credits and welcome bonuses of around $1000. They generally have a credit score requirement of 720.
If you're on active-duty status with the military, you could get special credit card perks and benefits.