I don't remember when DS stopped spitting up, but I use burp cloths now to clean him up after meals. Just dampen one, wipe him down and throw it in the laundry.
I don't have any real burp clothes but I used A&A blankets on my shoulder for maybe 10 weeks. I kept one in the diaper bag for a while after that just in case. I didn't have a spitter though.
I think the need dramatically reduced around 9-10 months. DD had reflux, I had 40 burp cloths. They are sitting in a basket in a closet. I plan to go through them, putting the ones that are worse for wear in DH's garage rag bin and the rest in our house rag bin, when I go through my baby stuff for my pregnant sis.
DS2 is 7.5 months and we haven't used them much in the past 2 weeks. I keep a pile downstairs just bc we literally went thru 5 a day everyday since about 4 weeks old. I think (hope) we are turning a corner in regards to spitting up. I always keep one in my diaper bag as well.
DS was a major "happy spitter." I used cloth diaper inserts as burp clothes. I used them until 10ish months. Set them aside for kid #2. Once DD is done with them I'll add them to our household rag pile.