It depends on the campaign.
Although I could say yes, since I have allowed subraces (who are from the MM, and from the FRCS, not from the PH).
I would allow in most campaigns:
* All subraces of humanoids, including orcs, goblinoids, and reptilian humanoids like kobolds. Exception: Troglodyte. I won't allow playing a character having a fixed alignment. PCs always have free will.
There may be some additional restrictions ("sorry, no drow") though.
* Some monstrous humanoids/fey/magical beast, on a case-by-case basis. One thing I'm willing to agree in nearly any campaign would be an awakened animal -- provided a player wants a character with a subservient role, as it will be considered more a "mascot" than a heroe in the story.
* Some of the lesser giants (but I don't see any of my players wanting such a character).
* Lesser undead (for a special campaign). Not vampire or lich, but why not a sentient, talking skeleton ?
ECL would be low. +3 seems a maximum to me. Playing something with a +4 ECL ? No.
This mean that some of the creatures would not be played as from the MM, but in a reduced version (notably, removing all HD, and making some of the race ability depends on levels; like a rock giant who would have his full rock giant strength only at level 10, for example).