* They've been dating for decades: The strip started in 1978, and they've been a couple since the very beginning.
* Their relationship is more of a background element: Jim Davis, Garfield's creator, has focused on Jon's awkwardness, Garfield's cynicism, and the cat's general antics. Liz is a secondary character.
* They've never shown any signs of planning a wedding: Their relationship seems stable, but there's never been any indication of a future together that includes marriage.
So, will they ever get married? It's impossible to say for sure. It seems like Jim Davis enjoys keeping their relationship status ambiguous. He could surprise us one day, but until then, it remains one of the great unanswered questions of Garfield!