Another trick I like to use to establish a better sense of fantasy and wonder in the campaign is to start things out very mundane and down to earth. Bandits will be humans rather than orcs. The owlbear stealing chickens from the local farm turns out to be a rival farmer in a makeshift costume. Magic is rare at first, and the real monsters wait quietly for the party to come to them, a bit later.
Certain monsters are so ubiquitous that using them is almost expected and doesn't do much to harm the mood of the game. Of course you wouldn't want a party of 1st level heroes actually challenging a dragon, but seeing one flying on the horizon at dusk, or hearing tales of his tyranny and gold lust are fine, even at basic level play. Orcs and goblins and kobolds (oh my!) shouldn't be overused, humans and demihumans are supposed to be the dominant races in the world, after all, but they can make appearances now and then without the DM screaming "THIS IS A FANTASY WORLD!" at the players. Remember, fantasy in the setting works best when you ease into it. Recall the wonder, excitement and trepidation of poor Bilbo Baggins as he ventures out into the world for the first time. Capture the wonder of Harry Potter as he prepares for his first term at Hogwarts school. The monsters, magic and epic tales of the setting will have a bigger impact on your players and be remembered longer and much more fondly if you build up to them. If you throw wave after wave of skeletons and zombies at the party from day one, there's no real thrill or shock when the BBEG (big bad evil guy, the primary villain in the campaign or campaign chapter) turns out to be a lich.
Consider as an example the Minotaur Cave encounter from B2: Keep on the Borderlands. This encounter, while fun and memorable, is flawed in two basic ways in my opinion. First, minotaurs are mythic, epic monsters, an encounter with one should be the climax of a lengthy quest involving a story reminiscent of the Greek tragedies from which the creature is borrowed. He shouldn't just be the pet and treasure keeper for a band of bugbears. Second, I think the purpose of the encounter, and the level of difficulty, can be just as easily fulfilled by replacing the minotaur with a bear. Use a Grizzly (or a Cave bear if you're feeling mean) and the encounter plays out similarly to the minotaur. The only difference in this case is that the bear wont have a reach/missile attack, so you might want to tweak the encounter area a bit to prevent characters from "shooting fish in a barrel" and picking him off from a safe distance.
This way, down the road when you have a great idea for an epic story arch that involves a minotaur, you haven't softened the impact of that creature. "Ho hum, another minotaur, let's get this over with".
I'm open to feedback and other ideas for maximizing use of the mundane and ubiquitous low level animals and monsters, so please use the comments below to chime in.
I'll leave you with a quote from Gary Gygax, from the aforementioned minotaur encounter in B2:
(the only options for escape are finding and using a secret door)... or else to run out of the place and climb a large tree.
Classic. I miss that kind of tongue in cheek humor in the game, WotC takes their D&D way too seriously.