"I don't want my world to be another generic fantasy world with generic D&D races!" you shout.
"Okay!" I shout, "Why are we shouting?"
How can you create fantasy races that are unique? (That includes, of course, fantasies that are modern or science fiction or any other setting - not just medieval fantasies.)
Stuck in a mental trap, you see every race you brainstorm up seems just like some other race somebody already made famous.
Let's go over a good way to create fantasy races.
Steal from Tolkien.
No, no, wait, I'm being serious. Instead of thinking "elves dwarves orcs hobbits", think about what those races mean to the story.
Each race is a lense to view the theme. In the case of Tolkien, the theme of the world can be thought of as "war against dark forces".
The orcs are those that have become dark forces. The dwarves are those that clashed and lost. The humans are those that are fighting right now. The hobbits are those that are getting drawn in. The elves are those that are above, that remind you that there is something besides the dark.
Quick and dirty, sure, but fundamentally the races can be thought of in that manner. Each race highlights a different part of the struggle, from a different angle.
This can easily be adapted to suit your own fantasy world.
For example, if your fantasy world's theme is "steam powered mecha fighting it out", you can create races to highlight it. In Tolkien fashion, you have a race that has embraced the abuse of mecha, a race that was destroyed after a long fight with mecha, a race that is currently fighting with mecha, a race that is beginning to fight with mecha, and a race that is above mecha.
From that you can expand the race into as human or inhuman a race as you want them to be. Classically, races in role playing games are pretty close to human, but every near-human variant is already established in your audience's eyes as a particular stereotypical race.
For example, our species that fought with mecha for a long time before losing and being destroyed. We can say that they would be adapted to fight in/with mecha. So they would be small (smaller pilots are better) and they would be good with machinery (repairing mecha) and they would be hardy (to live through smoke and steam and the steel mills).
Well, that's obviously fantasy dwarves, isn't it? Or maybe you could argue for gnomes. Either way, hardly original!
Now, if you want you could theoretically make them more unique by making them less human. But you have to go pretty far afield before you get to anything unique, and even then your audience will automatically lump them together with whatever popular race is vaguely similar. So even if we make our dwarflike people unique by letting them directly plug into their mecha through personal mechanical interfaces, now they'll just get called "borgs" or "shadowrunners", depending on the graphics we use to represent it.
Personally, I don't feel you have to make a race look distinct. They should look distinct enough from their other in-world counterparts, but it's basically impossible to come up with a visual that won't be automatically matched up with an existing, popular visual.
Instead, you should focus on making the race feel like a part of your world. Even if your races have exactly the same standard names - elves, dwarves, orcs, and so on - if they play a particular role in your world, they become a new and interesting species. And the main way to define a role is in how the species highlights your world's theme.
An example of this is Shadowrun, which has all the standard fantasy races, but uses them as lenses into the theme of a class struggle. This means that elves and orcs feel very, very different from Tolkien versions, because they represent elitists and the underclass rather than representing victory over and betrayal to dark forces.
There is no limit to the number of races you can create in this manner. Simply assign given regions different subthemes and make the races of that region highlight that theme.
For example, "steam powered mecha battling it out" might be a subtheme on the overarching theme of "use and abuse of technology". We could have another region which has the subtheme "oppression via technology", and create races for that. We don't want to use the same approach, because that leads to very samey races, so we might create lenses that highlight different actions that oppress, rather than different states of oppression. For example, we might have a race that specializes in surveillance, a race that specializes in computation, tracking, and paperwork, a race that specializes in "nonlethal" police actions, and so on.
This "theme-powered" method of creating unique races will result in races that feel unique and, more importantly, support the theme of your world intrinsically, making your world more immersive and profound.