I voted "no," though I'm tempted to unvote, as I suspect the question was somewhat ambiguous.
When I hear, "Do you restrict the playable races?" I interpret this as including an implicit "usually," or some other "almost all of the time"/"as a matter of general practice" kind of thing. And the answer to that would be a flat no. I'm not really a DM, but I like to think up story stuff a lot--and I never, ever specifically
intend to limit the number or types of races. I may do so if, and only if, it feels appropriate; if I wish to highlight the differences of the setting from a "typical" fantasy setting, for example, or in the rare event that I'm going for a heavily "historical" campaign and want that
bland, bland sweet, sweet "human only" feel

P).
However, on seeing many of the replies, it sounds like most people are interpreting the question as, "Do you
ever even remotely consider restricting the playable races?" In which case the answer would be a clear yes. It's always a potential consideration. I'm not going to deny myself a tool like that--I'm just, IMO, much more cautious with its use than most other people.
I do ban races if I have a strong theme I am going for (that I have discussed with my players before starting the game). One of my favorite homebrew settings is a Mediterranean game with (Greek) dragonborn, (Persian & Egyptian) tiefling, distant and scary (Roman) elves, and (sea people) humans.
See,
this kind of thing I think is just lovely. I generally prefer to extend this to be slightly more "cultural," e.g. there is the
Eusyccan League, where the dominant racial group is dragonborn, while tieflings are the significant majority in the
Sultanate of Al Beira, and elves are the bellicose leaders of the so-called
Lirian Republic (even though it's really been a
de facto empire for a couple of centuries now, its Senate being a vestigial organ). Not trying to say that you, mestewart, do or do not do this--just clarifying my preferences.
For a completely different example, I have long entertained ideas of...an "East-West fusion" setting, that is, one that melds or layers together both European and Central/East Asian influences. So, for example, the tiefling-dominant culture is inspired by the Byzantines; the mainly-orc culture is Nordic; perhaps the mainly-dwarf one could draw heavily on Indian subcontinent cultures (especially the caste system); the dragonborn-led empire is strongly influenced by Japanese and Chinese ideas both martial and political (e.g. Daoist-influenced political structures, supported by a powerful military caste a la samurai); perhaps the human-dominant cultures could draw on Saharan and Sub-Saharan Africa (I don't know these cultures well enough to give examples, but I'd do some research); since it's a bit of a trope at this point, the mostly-minotaur culture could be Aegean-inspired (e.g. Greek/Cretan) sail-centric; etc.
I also have a tendency to run on a "not yet, but perhaps" system, rather than a "no never" system. E.g. Q:"Are there gnolls in your setting?" A:"Not yet--but maybe! Perhaps Mirtul Khan has united the nomadic herding tribes of the west, and comes to bring terror and slaughter to the oh-so-high-and-mighty Lirian Republic."