Cuba was never annexed and the US forswore any annexation in the 1898 Teller Amendment.

Cuban support for annexation, once a lot stronger, had wained due to the development of a proto-national Cuban identity, born of the struggle against Spain during the independence wars.

The sugar lobby of domestic producers, like Louisiana and Hawaii (a territory, not yet a state at the time) were also very opposed to annexing Cuba since Cuban sugar would then flood US markets without any tariffs or restrictions, driving down sugar prices and potentially edging established producers out of traditional domestic markets.

One of the major impulses for Cuban annexaxionism had been that planters wanted to preserve slavery in Cuba, but the US abolishe slavery during the civil war and Spain abolished it in its colonies in the 1880s

Something to note is Alaska and Hawaii didn't necessarily apply for statehood immediately either, their statehood movements gained traction fairly close to when they achieved it (both in 1959), a while after the Philippines (1946) and especially Cuba (1898) gained their independence. As another commenter noted, Cuba was never intended to be annexed, and the Philippines, along with other major US territories, was meant to be a part of colonial expenditure and economic exploitation, NOT traditional Manifest Destiny.

https://www.archives.gov/legislative/features/hawaii/

http://avalon.law.yale.edu/20th_century/ak_statehood.asp

http://fcit.usf.edu/florida/lessons/s-a_war/s-a_war1.htm

http://historywired.si.edu/detail.cfm?ID=171