Yes, the verb "apetecer" is conjugated like "gustar".
No me apetece trabajar hoy.
No me apetezco trabajar hoy.
No apetezco trabajar hoy.
"No me apetezco trabajar hoy" is not correct, because the "me" implies that the verb "apetecer" is an action being performed on you, so "no me apetezco" can only be used without a complement and the meaning would be close to "I'm not craving myself". (Kind of creepy.)
"No me apetece trabajar hoy" and "no apetezco trabajar hoy" mean both the same, but the first one is expressed as if the will to do something did not depend on me and the other is more as if I determine my own will to do something.
By the way, the verb "apetecer" is far more common in Spain than in any other region, as far as I've seen.
In Mexico we would have just said "no quiero trabajar hoy" or "no tengo ganas de trabajar hoy".
