There are MANY ways to remove stuck and stubborn nuts/bolts, here are some of the ways that I've found work best.
These methods contain both simple options, and some that use luxurious tools such as an impact gun or welder. Use caution, as some of the methods described can cause damage to your parts and might injure you if you do not take proper safety precaution (read: don’t be stupid).
Step 1: Use Some Muscle
Try a 6-point wrench or socket on your seized nut/bolt. Start by rocking the bolt by tightening then loosing, this may be all you need to break through the rust. Try and avoid 12-point wrenches and sockets as they likely to slip and strip the bolt head.
Another great tool I have found that is made by Irwin Tools is there Original Locking Wrench. Found here
This tool has been a life saver for me! It has removed the worst brake bleeder screws I have seen! It works on rounded fasteners too. This beast can be tightened so much, that it will WARP the nut! These have been in my box now and will not be leaving any time soon! They have a parrot beak shaped jaw allowing 3 sides of contact without marring up the corners of a hex fastener! Neat, Isn't it??
Step 2: Clean It Up
If using some muscle on the bolt does not allow it to budge don’t be discouraged, as there's a few more ways to get that bolt free.
Take a wire brush and clean the bolt of loose rust and dirt. We will then use some PB Blaster or similar PENETRATING OIL (I can vouch for its effectiveness). Apply oil to the bolt and threads, covering it completely, then give it some time to work; I prefer to spray it every hour for 2 hours. It may work quicker or longer then that stated time, that is my preference. I’m impatient.
Now let’s try out the 6-point socket/wrench again, you may find that it now loosens easier but it may still bind. Again, rock it in and out to break that binding force.
Step 3: Leverage
Our next step is to use leverage to remove that stubborn bolt. Beware, rusted bolts and cheaper tools could possibly break and really screw you over. The best way to get some leverage is by using what is called a Breaker Bar, a long handled socket wrench without a ratchet mechanism. The longer lever will allow you to exert more force by being able to lean into it AND have excellent leverage, this will multiply your strength on the bolt. A lot of times, this will work for you.
Another way to get leverage is to use your wrench or socket wrench and add a pipe over the handle as an extension. However, the wrong tool for the job could hurt you. I suggest you do it right and buy a breaker bar.
Beware, at this point if your bolt is beginning to feel "soft" it may be twisting and about to break.
Step 4: Heat 'er Up
At this point, the bolt may still not budge. I bet your getting frustrated, Right? Don’t fear, there’s still plenty more things to try!
Our next step is to use a torch to heat the bolt up. The idea is to have one side of our bolt expand from the heat and break the rust. This can be easily done with a small propane torch. Be careful, this method WILL ruin the heat treatment on stronger bolts.
Heat it up as hot as you can get it without melting the bolt. Remove the heat and let cool or pour warm water on the bolt to speed up cooling. Once it is cool, try out the breaker bar again. With any luck, The heat has broken the rust seal on the bolt allowing it to turn.
This is not a good idea around flammables or rubber gaskets/bushings.
Step 5: Be Smooth
Since we have the propane torch out, we can also add candle wax to the stuck bolt threads. Apply a paraffin candle to the cool side of the nut, this will allow the paraffin (a lubricating wax) to be drawn toward the heat through the threads allowing you to unscrew the nut hopefully.
Step 6: Home Chemistry
If that has failed, our last attempt to do this without harming the nut and bolt is to treat it with another penetrating agent one last time. However, this time we will mix up our own.
Try a 50/50 Mix of Automatic Transmission Fluid with Acetone; it works exceptionally well. Treat several time over an hour and try to loosen again with the breaker bar.
Any luck? Time to do this the hard way!
Step 7: Drill a New Hole
If you have been unable to free the bolt by now, we'll have to take drastic measures.
If we are working with a bolt, We will have to drill out our bolt and retap the threads for a new bolt. This involves picking a drill bit the size of the hole, boring straight in and removing the threads of the bolt. Then, you will need to screw in a tapping tool to recreate our threads. If you need the exact size hole, bore the bolt out oversized and buy a heli coil. This threads into a tapped hole with an inner diameter for the correct bolt you would like.
Fortunately, a nut is much easier to remove.
Step 8: Split a Nut
If you have good access to the bolt another option could be to use a nut splitter. These inexpensive gadgets are found at most at most auto parts stores - I paid $10 for mine.
A nut splitter is slipped over the seized nut, then a screw on the side of the splitter is tightened which forced a wedge into the side of the nut. Keep cranking the nut splitter screw until the nut makes an audible pop and you get through the nut. Back off the nut splitter screw and clean the bolt of the split nut. Try adding more penetrating oil to the newly exposed bolt threads, then use one of the other methods described above to remove the bolt. With the nut removed, the bolt should be much easier to remove.
Unfortunately, this method destroys the nut and every once in a while the bolt too depending on its condition.
Step 9: Be Abrasive
Our last step if the nut splitter doesn’t work (or appeal to your stubborn bolt scenario) is use an angle grinder to cut the head off the bolt. Simply grind the nut and bolt until the nut no longer exists and pull the bolt right out.
This works great just be very careful as angle grinders can be a dangerous tool, they spin exceptionally fast (8000+ RPM) and have no anti kick mechanism. If your are not careful, the grinding disc may shatter and fly apart in all directions. The grinding also produces a lot of heat and sparks. BE CAREFUL!
Step 10: Bolt Extractor
Oops! You just broke off the head of the bolt you were trying to extract, leaving you with a stuck bolt and no way to remove it. Luckily there's one last way before drilling and retapping.
Go to an auto parts store and look for a Bolt Extractor, it’s a nifty tool that screws in the same direction as the bolt unscrews and allows you to drill into stuck bolt and keep turning it tighter and tighter until the bolt comes free and out. My bolt extractor kit came with a reverse-threaded drill bit, allowing you to drill into the bolt and then back the bolt out using the bolt extractor. It's a GREAT TOOL and will save a lot of headaches
Step 11: Feel the Vibes!
This a relatively new method I have learned from a friend of mine! I wanted to add this to the list. A great way to remove a stubborn bolt is to "shock" it loose. When I say shock it loose, I mean hammer it! To be more precise, an Air Hammer. Using an air hammer on low pressure will make a nice vibrating but strong tool enough to loosen rust sometimes. Believe me, It works. If you tune the air pressure correctly, It will have a distinct hum. On the other end of this spectrum, if the first doesnt work, is to use a blunt or pointed tip on the head of a bolt with full PSI to the tool. This rapidly hammers it breaking the rust up mechanically. Even greater when penetrating oil has been applied. I have found this works very, very well. To my recent discovery, There is actually a brake bleeder tool made by Phoenix Systems called a Bleeder Buster. It works on the basis of a hammer action while putting rotational force on the stubborn bolt! I got a set from them, and I can confirm that it works very well!
Step 12: Dont Go Nuts!
Another option for removing a rusty and stripped bolt? You can always repair the hex portion of the faster! How? Its simple! A great way to do this is to add a new nut to the old bolt head! A great way to do this, is to use a wire brush to clean the head of the bolt. Pretty clean is acceptable. From here, An appropriate sized nut can be MIG/Wire Feed welded on top of the bolt to provide a new gripping surface for the wrench onto the bolt! Nifty eh? Well, Guess what! This heating to cherry read while welding is also a great heat shock to the corrosion holding the fastener on! This makes it easier to remove!
Step 13: Brace for Impact!
One last tool I use often in my own work, Which is a life saver if you have it, Is an impact gun! Be it battery, corded, or an air impact tool! Heck, Even manual impacts work! These tools focus on a power and fast rotational hammering action to shock and loosen the bolt in one motion! They are much less likely to round off a bolt then using a breaker bar! However, They tend to occasionally snap rusty bolts off unfortunately. Use with care, Especially if you have a powerful one! There is not much to them, Simply put them on a rusty nut and depress the trigger and let the tool hammer away!
Step 14: Thanks for Reading
These are all methods I’ve used personally and have found work for me, I hope this has helped make the frustration and difficulty of stuck nuts and bolts a thing of the past for you.
I look forward to seeing comments here on other ways you have found that works too! I'd love to add some more ways if you have any of your own.