I actively avoid anything Cage is in. That said, Leaving Las Vegas was a masterwork.
Recent ones: Both Renfield & The Unbearable Weight of Massive Talent were both really fun amid a lot a terrible movies over the last 15 years.
Haven’t seen Raising Arizona; probably should as I like the Coens.
Matchstick Men.
Raising Arizona, with Moonstruck as a close second.
Mr. Cage has said his favorite is Pig.
My choice is National Treasure.
I guess I’ll be the first to mention Honeymoon in Vegas (1992). Not as well known as some of his others, but a perfect role for him.
A couple of my favourites (quoted straight below) have already been mentioned but I’m going with Adaptation (2002).
We just watched it again about a week ago, and it really holds up. It’s probably tied with Raising Arizona as my fav.
Snap out of it!
It wasn’t at the time, but watching Moonstruck recently, it now feels like a very well made timepiece.
Another vote for “The unbearable weight of massive talent”. Also a big fan of his first Ghost Rider movie.
Another vote for Raising Arizona; I’m not sure if I’ve even seen the others mentioned (but did like the movie a lot anyway).
Valley Girl. No brainer- applies to my choice and the movie.
Raising Arizona. No question.
In my opinion, the best part of that movie was the soundtrack.
It’s one of the all-time greatest romantic comedies, IMHO.
It’s a tough call between Raising Arizona and Moonstruck. They are both outstanding movies with great casts. I think I gotta give the edge to Raising Arizona.
Raising Arizona is my favorite, but I have a soft spot for Honeymoon in Vegas, even though objectively it’s a pretty mediocre movie.
I was going to list that one. 
Not sure I’ve seen very much at all that he was in. No objection to the actor himself, the movies themselves didn’t seem to draw my attention.
IMO, there’s a place in life for the occasional no-brainer movie just for fun. Not everything must be excruciatingly deep and profound.
“Pig” was excellent.
There is a fine line with Nicolas Cage movies that you love despite being objectively uninspiring, and the sorts of movies that support Nick’s style are often unsophisticated shall we say.
So my list isn’t “so bad I loved it” but I’m not going to hold them up as his best roles or highest quality movies.
First, of all I considered.
When Peggy Sue got married: My first Nick Cage movie, and admittedly, he’s more a supporting actor but not a Cameo.
Raising Arizona: Good movie, didn’t quite mesh with me, but lots of fun and quotable bits. Like it a lot, don’t love it.
Moonstruck: My generation saw this as a “Chick flick” ( I was 11, so, duh) so I appreciated it a bit later, but not a fave.
Skipped ahead to the next generation of his films and a few actual candidates for me:
The Rock - a favorite movie, and I love a lot individual parts with Nick, but it’s much more about how perfectly the cast interacts as a whole. While Nick works well, almost any competent actor could have done nearly as well in his character’s position.
Face/Off - Okay, now a contender! Yeah, the premise is unspeakably stupid, but I love how both characters swap roles and manage to do so in an interesting way within the suspension of disbelief.
And then a few of of the more recent, and ones that click best with me:
Mandy - first of two “near silent” protagonist films. I love Mandy beyond reason, trying to piece together what may be real, what may be illusion, and how much of it all may just be dreams in the mind of an isolated girl. It works with with the traditional Low affect to High Energy Cage acting. Probably my favorite that I’m not embarrassed by.
Five nights at… ahem, sorry, no, I mean Willy’s Wonderland - probably my favorite that I’m still somewhat uncomfortable to admit. The movie isn’t terrible, but absolutely closer to “so bad it’s good” than I want to admit. But it 100% connects with my 80’s childhood of slasher movies with thin plots, watching the rest of the team getting picked off, while Cage’s utterly silent protagonist just wrecks everything else in sight. Nearly neck and neck with Mandy, but the madness and dreamlike quality of Mandy put it over the edge for the win.