RACE:
At campaign start I'll sometimes force the race, based on where they're starting out; and other races can join in later.
Barbarian in my game is a sub-race of Human, not a class, and always will be.
There are no Halflings in my games. There are, however, Hobbits.
Otherwise, for races I don't tend to outright ban things but if you want something uncommon (this includes Gnomes) you have to risk rolling on a racial abundance table and being stuck with what you get; you're most likely going to end up with one of the basic races anyway but (un)lucky rolling can get you into a Leprechaun, Hobgoblin, Dryad, Sylph, or a bunch of other quasi-playable races. You can also get into some unusual versions of standard races here - Gray, Arctic and Dark Elves, for example.
I can't see myself ever allowing Dragonborn or Tieflings in any game or system, ditto Warforged unless I for some odd reason was running a steampunk campaign.
CLASS:
I have 14 classes in my game - Cleric (War. Normal, Nature-a.k.a.-Druid), Fighter, Cavalier, Paladin, Ranger, Magic-User, Illusionist, Necromancer, Thief, Assassin, Bard, Monk. That's it. A few specific race-class combinations are banned - there are no Dwarf Wizard-types, for example - but I'm way more lenient than RAW 1e ever was; and most of the old racial level limits are long gone too. That said, I think if I ever start another campaign I'm going to put a few restrictions back in.
Paladins aren't banned but they are somewhat discouraged by...
ALIGNMENT:
...any alignment being allowed, and played. In my current campaign PC Necromancers in total have outnumbered PC Paladins 3-1 (and there's been about 6 PC Assassins as well, mostly multi-classed with something else); and if the party want to fight each other instead of the enemy it's all fine with me.
PSYONICS:
After years and years of trying to make them functional but not broken, I finally ditched them for PCs and most monsters. Some iconics e.g. Demons, Mind Flayers, etc. still have them, and are thus even more dangerous.
Lanefan