Yes, I specoialise in Short cross and have around 100 at the moment. Probably around half are cut halves, which I only buy if they are cheap, in good condition and I can identify the mint and moneyer. I have picked up examples from the rarer mints that way, such as Carlisle, Worcester, Rochester and Wilton and of course Rhuddlan.
I have quite a few voided long cross (Henry III) and long cross pennies (Edward I-III) too and some other hammered pieces from various kings, a few groats and some Commowealth pieces. Oh, and I have a collection of milled crowns too.