Removing Everything Else
There are several types of jewelry that I either don't stock or don't recommend for piercing. Though I do stock and suggest plugs with o-rings, I'm not a big fan. They tend to be easy to put in and take out, but unless they are grooved, the O-rings tend to slide off. This can also be a problem with even jewelry that has grooves. Removing the jewelry is relatively straightforward. Removed the o-ring and then slide the jewelry through the piercing.
What I'm also not a fan of is flanged jewelry. The reason is that putting the jewelry in and stretching a piercing well beyond its current size can cause damage to the piercing. Once they are in, they will stay put until the piercing begins to pull again, and then they start falling out. I strongly suggest doing a soak, applying a compress, or, at the very least, taking a hot shower before attempting to remove the jewelry. Soaks and compresses should be done with a mixture of sea salt and warm water. 1/8 to 1/4 teaspoon per cup or 8oz of warm water. Soak is done by inverting a small cup over the piercing area or submerging the piercing for around 10 minutes. For piercings where it is not possible, use a folded clean paper towel or sterile gauze sponge to soak up the liquid and lay it against the piercing area. Re-submerge the compress when it cools and apply it for roughly 10 minutes. This will make the tissue more flexible and easier to stretch. When removing flanges, it's essentially force that removes them. This involves slowly pushing and turning the plug on its side, and then sliding it out.
Nostril bones are another jewelry style that I suggest against. They are a stud with a ball on one side and a charm of some kind on the other. They usually slid right in because the ball is roughly 18g, which is the most common size for Nostril piercings. The problem is that the post is usually a thinner gauge. The body conforms to the post thickness, making removal a problem.
In some cases, cutting the wire is the only way you can remove them. I strongly suggest doing a compress, as mentioned above, before attempting to remove the jewelry. This will make the tissue more flexible and easier to stretch. To remove the jewelry, grab it on the outside and pull. Hopefully, the ball will slide through the piercing. If you are one of the unlucky ones who can't get it through, I would suggest cutting the jewelry with wire or tin cutters. Another option would be the inside area of a needle-nose nose of pliers. Cutting should be a last resort and should only be done if you have no other way to remove the jewelry.