I am installing new spark plugs in my 2013 Chevy Cruze and I dropped a spark plug in the well upside down. I tried to get it out with 8" needle noose pliers but it will not budge. Any help would be appreciated.
It may be, since the plug is upside down, the porcelain of the plug may be stuck in the threads of the spark plug hole. If this is the case and it is in there tight enough not want to budge, you may be able to knock it free using the piston by rotating the engine.
I'm going to assume the sparkplug hole is directly inline with the cylinder, directly over the top of the piston. By rotating the engine, the piston should come up far enough to gently touch the sparkplug which is sticking down in the hole. By moving the piston up into it, you'll knock it free of the threads, which should allow you to more easily grasp the plug with which ever method you use (take your pick from the other posts, as most are reasonable). This may also push the plug up far enough to more easily grasp the electrode end.
As @cory suggested, do not reuse this plug. There are too many ways it may no longer be serviceable, it doesn't make sense to even try it. Replace it with a brand new plug and know it's golden.
The first thing to do it to be sure that the well is wide enough to allow the pliers to open up enough to actually grip the plug, you may only be able to grab it by the electrode. You probably don't want to try to grab it by the outside of the threads because there may not be enough room for you to pull it up if you do that.
Assuming that you're grabbing it by the ground electrode a bit of gentle wiggling should be enough to get it to come free. There is nothing that should be catching the plug and holding it in (but double check that, I'm saying it doesn't seem like there is anything that should be trapping it, but if it seems like something might be trust that), so if it really won't come then it is time to rethink the strategy.
It could be that you're not able to open the pliers wide enough in the well to grab the electrode, if that is the case you might try getting a fine piece of wire and make a loop that you can use to snag the ground electrode.
I think one of the listed solutions should get the job done, but there's one thing I have not seen mentioned. Once the plug is out, examine the ceramic insulator carefully. If there are pieces missing, look for them in the well. If they are not there, they are likely inside the cylinder. To confirm that there are pieces in the cylinder you can use one of the scopes that let you see the inside of the cylinder. You may be able to borrow one from some parts stores, or buy one fairly inexpensively.
Just be careful you don't run the engine with bits of the ceramic in the cylinder. If it gets lodged in a valve or somewhere else inconvenient, you could cause really serious damage.