What are some causes for sore, swollen gums?

Many reasons. Gum disease causing gingival inflammation. Localized bone loss causing improper drainage leads to swollen gum. Food impaction leads to swollen gum. Periodontal abscess. Tooth abscess with draining tract along the gum. Localized trauma. See your dentist to treat the cause, not the symptom.
Most common... The most common cause of sore swollen gums is gingivitis or periodontal disease, both related to poor oral hygiene and not having routine cleanings by a dentist. However, there are many other causes both medical and dental. See a dentist for a complete and thorough examination and evaluation.

Related Questions

Having swollen gums after dental bridge removal. Really sore and painful. Should I take any medication?

NSAIDs. OTC pain meds should take care of your discomfort. Really can't tell if you have an infection over the internet. Give your treating dentist a call for further guidance.
YES, Ibuprofen. Yes please do take some medication...NSAIDS work best and I prefer ibuprofen for my patient as long as they don't have any medical conditions or allergies issues. You can also do a warm salt water rinse to sooth the tissue.

My teeth are rapidly falling out, I have swollen gums and my mouth is sore. What could I have?

Periodontitis. Periodontitis or gum disease started with bacteria that is left on teeth and gums. This caused an infection around the gums and other supporting structures of your teeth. Eventually the bone around the teeth is damaged and teeth become loose. When the damage is severe, all teeth must be removed and dentures placed. Sometimes this chronic infection can affect other parts of your body, heart, kidney.
Sounds like. You have generalized severe periodontitis -- simply put - severe bone loss resulting in un-supported teeth, hence loose teeth, gum inflammation and infection. I recommend you be seen by a dentist as soon as possible for treatment.

Swollen gums, drooling, fussy, behaves as if trying hard to poo (2days back got sore bottom due to hard stool but now it's soft)teething? Shd I see a doc

If you are worried. Then yes see a doc. It sounds like teething and constipation. Hylands teething tablets or humphries #3 can be awesome for teething discomfort. Constipation can be relieved by stopping dairy, increasing p fruits (peach pear plum prune pineapple pumpkin peas and pomegranate). If these dont work or you are concerned than yes see your pediatrician.
Need 2 exams. Except for gi, symptoms probably due to teething, but never hurts to have pediatrician take a look. Also, must make 1st dental appointment with dentist, or preferably pediatric dental specialist.