
Melee:
Baseball Bat (Everywhere)
Cobb's Bat (3 baseball bats tied together)
Baseball Bat w/ Barbed Wire (Can't remember)
2x4 Plank (Everywhere)
Butcher's Cleaver (Meat Market, Chinatown Restaurant, Coney Is. Cafe)
Switchblade (Everywhere, can be bought from blade dealers)
Sledgehammer (In front of skill-tester thing near Twiggy's shop, Vodoo Motors, Hardware shop in Riverside)
Lead Pipe (Everywhere)
Crowbar (Everywhere, Usually in Hardware shops)
Crutch (Drugstores)
Police Baton (Carried by all cops)
Electric Guitar (Music shop in Riverside, The Red Devil)
Acoustic Guitar (Music shop in Riverside)
Machete (Riverside alleyway, abandoned petrol station in Tremont)
Broken Beer Bottle (Aquired after beer bottle is broken over somebody's head)
Brick (Everywhere)
Sword-Type Thing (I've only seen it during Rumble Mode at the Shao Lin Temple)
Pool Que (The Destroyer's Hangout, The Red Devil)
Chair/Table Leg (Everywhere, found after breaking a table/chair)
Broom (Inside various shops)
Saucepan (Inside various restaurants)
Wok (Inside Chinatown restaurant)
Plunger (Inside Plumbing Shop)
Shovel (Inside hardware shop)
Update: Wrench (Everywhere, inside pllumbing shop and hardware shop)
Projectile Weapons:
Brick (Everywhere)
Glass Bottle (Everywhere)
Small Speaker (Shop fronts in Riverside, next to truck near the Destroyer's Gambling Pit)
Small T.V (Same as above)
Cinder Block (Everywhere)
Small Bar Stool (Most clubs)
Large Bar Stool(The Red Devil)
Chair (Inside most shops, inside most hangouts)
Small Paint Can (Shop fronts in Riverside, Chatterbox's Gallery)
Radio (At "Parties", inside the Warriors hangout)
Donut (from the kiosk during "Feed the Bums"
Salami (From Meat Market during "Feed the Bums")
Chicken (Inside cabinet at the Meat Market)
Steak (Same as above)
Ice Cream (From Ice Cream kiosks)
Skull Candle (Twiggy's Shop)
"Vase" (Lol, Twiggy's shop)
Foam Finger (Twiggy's shop)
"Suds" box (Laundromat)
Clothes Basket (Laundromat)
Trash Can (Everywhere)
Cardboard box (Everywhere)
Bundle of Newspapers (Everywhere)
Rubbish Bag (Everywhere)
Molotov (Everywhere, in the cabinets in the liquor stores)
Coffee Mugs (Found in the donut shops)
Cash Register (Inside most shops - Note: If the cash registers are punched/thrown against a wall 3 to 4 times, they will open and you can grab the money which is inside, usually quite a bit:) )
Update: Drum Kit (Inside the Red Devil)
Update: Bag of Flour (Chinatown)
There is also the Revolver and the Mace (Pepper Spray) which feature in the game, but cannot be used by the player

If you can think of any I've missed, please let me know. I hope this helps.