A terrible buzzing, huge insectile wings. A massive chitinous hide, a slender neck topped with a terrible reptilian maw with a single serrated horn atop it. Two huge pincers lash out at you and as it draws close it brings it's body close against you, a terrible circular mouth filled with triangular teeth rests in the center of its chest. It's terrible eyes glow brilliantly before beams of horrible multicoloured energy flow from the compound orbs and tear through your companions.
What monster is that? What are its weaknesses? What else can it do? Mystery, suspense, maybe even fear. The truth is, the monster described above is nothing more than a CR 7 chimera. Right from the bestiary. The change is purely cosmetic. No templates, no cr adjustment, no extra HD, just describing your monster in a new and different way can make it a brand new threat that catches the attention of even experienced players. This gives you freedom to add variety to encounters, or to build a theme in your adventures. If your dungeon is the lab of a mad alchemist and you need more terrible abominations to use just grab any old cr appropriate monster and mess it up! This can also be used to make a region of your campaign feel more exotic and unique without taking a ton of prepwork.
With that said, it's certainly possible to make a few basic adjustments to make a monster even more different. Replacing a monsters natural attacks with different ones with the same average damage, switching up energy resistances, damage reduction, and regeneration , or even altering the type of damage a monster deals can help enhance the illusion of a totally new monster without altering game balance at all.
If you are going to make major cosmetic changes to a monster though just be aware that your players are going to want to know what it is. I like to keep things mysterious with my players, so I don't tell them when I use this method. But other DM's may enjoy sharing some tricks and tips with their fellows to encourage them to get creative and look at each foe with a new perspective. Along with curious players a DM should also be wary of curious players. The confidant DM turning the horrible insect beast above on their players can quickly become a stuttering unprepared shyster when the players start calling knowledge checks to identify the creature and the DM has no answers. So be wary that you might need to explain yourself, although personally I think once in a while it's fine to tell a player that they simply cannot identify a creature, regardless of bonus as long as that doesn't happen more than once every few sessions.
Of course along with this basic premise I also should acknowledge that some monsters might not need it. A chimera is pretty scary all on its own, even without making it a new monster, as long as you describe it well it can still drain a little colour from your players cheeks. The mystery might not be there, but there's still lots to fear from the traditional monsters, plus with such a plethora of monster books availible there's no trouble finding something your players have never seen before.