Just to be crystal clear on this...mostly all homes are purchased CASH, we are all "CASH buyers"...its just that most buyers use a mortgage instrument to obtain the CASH to give to the seller. Buyers who need a mortgage are technically CASH BUYERS. If you DO NOT NEED a mortgage to obtain the cash, i.e. you actually have all the cash on hand, you will not have a problem buying a home.
Its worth mentioning that you also can purchase a home without cash if someone is willing to take some other item that you have. Example could be swapping a home for another home (that is owned free and clear), or valuable jewlery, antique car etc...these types of transactions are few and far between..In real estate everything is negotiable.