The barghest, best known for its ability to eat souls to gain more HD. It should be obvious that any DM planning on allowing Barghests should impose some kind of restriction on this: I myself recommend using the Feed ability as an alternate form of advancement, with the barghest being able to add another RHD (leading to eventual development into a greater barghest) on levelup rather than a class level presumed it has consumed an appropriate number of souls. That said, it's worth an asterisk in my opinion.
Why play a barghest? Well, they have six outsider HD, good stats all around, a few (admittantly weak) natural attacks, DR, scent, darkvision, spell-like abilities and the power to change shape.
The shapechanging is fairly unimpressive: being a wolf is only useful for traveling and tripping, and turning into a goblin will lower both weapon damage and size modifiers, making melee combat far less interesting.
The spell-likes scale with your HD, but are otherwise not great. Blink is perhaps most interesting, but it requires you to spend an action every few rounds and harms you too, and Misdirection and Rage have been available to casters for so long now it's not even funny anymore. The 1/day abilities are better, but not exactly beyond an equally-levelled caster's reach either.
I find myself wondering what to do with a barghest, honestly. Melee seems the wisest, and a martial adept can still reach 8th-level maneuvers, but the racial abilities don't synergize so well. I guess one could make this work, but can't help but think of any barghest character as a misshapen combination of a caster with poor spells and a fighter.
Still, I can't help but see the creature's potential. +1* LA seems just appropriate, if only because of the relative strength of outsider HD.
Basically a barghest with bigger numbers. It can assume a Large goblinoid form (ask your DM what the exact stats are), which should allow you to wield weapons... except by then you might as well play a half-ogre or goliath. The higher ability scores and larger number of spell-likes are decent, but again: they're just bigger numbers.
Is the LA still warranted here? I'm not sure: most of your tricks can be duplicated rather easily by now: even Barghest's Feast is only two levels away. +0* LA it is.