While there are a lot of hotels and hotel chain-branded credit cards, only few of them offer an annual award night without specific spending limits set. Here is the full list:

Chase IHG Premier – free night in hotels up to 40,000 points. Annual fee $89.

Chase World of Hyatt – free night in category 1-4 hotels. Annual fee $95.

American Express Marriott Bonvoy Brilliant – free night up to 50,000 points. Annual fee $450.

American Express Marriott Bonvoy Business – free night up to 35,000 points. Annual fee $125.

American Express Hilton Honors Aspire – free weekend night excluding these properties. Annual fee $450.

(24 March 2019, new cards added:)

US Bank Radisson Rewards Premier – 40,000 points annually, good for standard room up to Category 4 hotel (or 4 nights in Cat 1). $75 fee.

US Bank Radisson Rewards Business – 40,000 points annually, good for standard room up to Category 4 hotel (or 4 nights in Cat 1). $60 fee.