Some of the most memorable monsters I've ever seen or used have been those that actually thought about the question "What does it want?" Monsters that are basically just animalistic "it wants to eat the PCs" kind of have a disadvantage here -- they can be used well, particularly with Hobo's advice, but contemplate the effectiveness of a monster that wants something not immediately obvious to players.
This obviously favors sentient monsters more, but there's something to be said for having even animalistic monsters behave in inobvious ways. The classic bit of gryphons wanting to eat your horses, not you, is one aspect. What about the troll that wants a husband? The manticore that plays butcherbird, building a larder of impaled corpses around its lair? The ghoul family that wants to "adopt" a new baby? And of course, when you're dealing with social, intelligent monsters like vampires, there are all kinds of motivations you can play with other than "find pretty victim, drain, repeat."
Yeah, it's definitely a thing that players can get a little over-familiarized with monsters. However, I think that's only one part because they get used to the monster; the other part is getting used to how it behaves. In some ways I think a familiar monster that has a new, fresh context is preferable to a brand new monster: it gives players enough recognition factor to immediately register an emotional reaction other than bewilderment, but still has that exciting tinge of the unexpected.