this thread had been beaten to death enough already, but i want to add a few things. i'll say up front that i'm not an electrician, but last year i remodeled a small garage into a workshop, and did all of the work myself. i did a lot of research and found out a few things i did not know, and i suspect some of the posters here do not either:
1. if a welder is tripping a circuit with 14/2 wire and a 15a breaker, even if you only bumped the breaker up to 20a, it might work without burning the house down. the moment the draw is over 15a, the breaker tripped, but the wire did not catch the house on fire. this is because it takes a certain amount of time for that wire to be overloaded to the point of failure. this effect is even allowed for somewhere in the code. i've read about a case where a circuit for a welder used a 50a breaker, but only #10 wire. this is acceptable because the duty cycle of the welder will not allow sustained current for long enough to cause a fire. i was also told this breaker oversizing is common in hvac systems with high startup draws but low sustained draws. i've only heard about this with 240v circuits, so i do not know if this is acceptable by code with a 120v circuit. i believe it also requires signage on the receptacle noting the duty cycle/usage. this is certainly a case for an electrician, but i wanted to make this point.
2. cable for extension cords is labeled with the total number of conductors, so 10/3 is going to have 3 conductors, while 10/3 nm cable will have 4 conductors. if you read the fine print, nm cable will often be listed as 10/3 with ground. that's the 4th conductor. if you are making an extension cord for a 120/240v use (newer generator hookup, etc) you will need a xx/4 (insert your own cable size) cord.
3. someone mentioned replacing the wire with 10/3 so there was a neutral. unless the appliance uses BOTH 120v and 240v, your circuit will have 3 conductors only. a 120v will have a separate hot, neutral, and ground. if you have a 240v only circuit (like most stick welders) you tend to think of it as two hots and a ground. technically, you have two hots, two neutrals, and a ground. many people don't think about it, but these circuits need neutrals to complete the circuit. they DO NOT conduct electricity through the ground unless there is a fault condition. each of the hot wires also acts as a neutral. when one hot lead is delivering current, the opposite hot is acting as the neutral. when the current cycles, the two hot wires reverse roles.