With the word traditionally spelled analogue, American writers tend to drop the silent -ue in some contexts, making analog. The spellings are largely interchangeable, though analog is usually used in relation to electronics, while analogue is often used in the sense something that bears analogy to something else. Outside the U.S., analogue prevails for all senses of the word.
A similar trend has changed the American spelling of catalog (formerly catalogue), but other words ending in the silent -ue have not yet undergone the change. For example, dialogue, monologue, epilogue, and pedagogue are still the prevalent spellings, though the shortened forms do pop up occasionally and may continue to gain ground.
American publications tend to use analog in relation to electronics:
4K TV doesn’t change the viewing experience as fundamentally as the shift from analog to HDTV. [LA Times]
Then, of course, analog went away, and so did the rabbit-ear TVs. [Washington Post]
And they often use analogue in contexts unrelated to electronics:
A whole roasted fish is the aquatic analogue to roast chicken. [New York Times]
The offline analogue is Occupy Wall Street. [Wall Street Journal]