Here's some of the things we've started, and not started since the public beta came out:
SKILLS
Defence (You can get hit 0)
Thieving (You get the right amount of money, you get stunned and you can thieve almost everything)
Runecrafting (Talismans' work, abyss does not work yet, you can craft most runes)
Magic (Most attack spells work, curse spells still in development)
Prayer (You can level, but the spells don't function yet)
Woodcutting (You can cut all most known trees: Normal, Oak, Willow, Maple, Yew and Magic)
Firemaking (Same as woodcutting, you can burn all logs)
Fletching (Not started yet)
Range (Bows work, not sure about cross bows, you get some of your arrows back when you shoot a bow, knives, javs, thrown axes and darts don't work yet)
Strength/Attack (You can hit higher with Strength, and more accurate with attack)
Minning (Most minning spots work, still in development though)
Summoning (Works in the private beta, not public yet)
Smithing (Does not work yet)
Fishing (Does not work yet)
Cooking (Does not work yet)
Farming (Does not work yet)
Crafting (Does not work yet)
Slayer (The slayer monsters exist of course but Slayer its self does not work yet)
Agility (Does not work yet)
Herblore (Monsters drop the herbs, but you needed to start a quest to get level 3 herb to even start herblore)
Hunter (Does not work yet)
QUESTS
None of them work yet
WEAPONS & ARMOUR
Most basic armour and weapons work (Bronze-Rune, not sure about dragon, barrows ect.)
MINIGAMES
Castle Wars is in development
SHOPS
2h sword shop
Platelegs/plateskirt shop
Port sarim jewelry shop
Varrock runes shop
Varrock platebody shop
Lumbridge axe shop
And some more that I forgot
Nice Unofficial List, X. Shows that you put in initiative. :)
Runecrafting: Getting 2/3/4x the runes for a higher level per essence works. "Locate" option on talismans works.
Magic: Teleport spells work, but I'm pretty much the only one with a high enough Mage to actually use them. =D
Prayer: Bones like Dragon Bones can be buried/give more experience than normal bones.
HIGHSCORES
Highscores work. There are personal highscores for single players, comparing players, and searching by rank. Some "Rank"s are messed up because admins have higher stats but are hidden.
For now, the highscores shows bug point totals for players too.