How do I obtain all of the weapons. I have only been able to locate the Polar Star, Machine Gun, Fire Ball, Missile Launcher, and the Bubble Gun. I have heard about the Spur, but I don't know how to get it. How do I get that, and, are there any others (if so, how do I get them).
Obviously all of these are going to be put in spoilers...
Take a bottle of Jellyfish Juice back to Mimiga Village and use it on the fire in King's house. You'll reveal the Bubble Gun.
Get from Santa after rescuing him
Trade the Polar Star to Curly. Locks out the Snake and the Spur.
I think you can actually miss this if you don't talk to King after your battle with Mutated Torako.
Trade the Fireball and Polar Star to the bug mechanic in the Catacombs. Locks out the Spur.
With the Booster 2.0 and the Polar Star, return to the cave you start in at the beginning after fighting the Island Core for the first time and returning to the deserted Mimiga Village. Once you reach the Gunsmith who you got the Polar Star from and give it back, he will transform the Polar Star into the Spur.
Find the tiny man in the Mimiga Village graveyard (Should be near the knife-weilding enemy) after talking to his family underneath the outside side of the island (just to the right of Dragon Egg 00 in the Egg Corridor). Take him back to his family, then talk to him. He will offer to trade you the Nemesis for King's Sword.
Alright, here is a list of all the optional weapons in order of appearance:
Talk to Santa after returning his key.
Use Jellyfish Juice on the fireplace in the Assembly Hall
Talk to Curly in the Sand Zone Residence. Trades for the Polar Star. Can't obtain the Snake or Spur.
Talk to the Gaudi 'Chiba' in the Labyrinth Shop. Trades for the Polar Star and the Fireball Can't obtain the Spur.
If you ignored Professor Booster in the Labyrinth he'll give you the Booster 2.0, use this to fly back up to the First Cave and talk to the Hermit Gunsmith. The Polar Star becomes the Spur. You can talk to Chiba from the Labyrinth Shop to get the Whimsical Star.
In the Outer Wall there is a house below the platform where Kazuma is. Using the Booster fly into there and talk to the person who asks: Now where did that man run off to... You haven't seen my husband, have you? Or if you have Cave Story+: Where'd that husband of mine go... Have you seen my husband? After talking to her go to the Graveyard/Cemetery and look for a small green man in the grass, talk to him and bring him back to his house. He will offer you the Nemesis. Trades for the Blade. There's an Easter Egg if you complete the game without taking the little green man home.