Cash — Cash is king, but not always. Cash is only king when cash is either needed or when cash trumps a bigger potential strategy.
Stock — This could include private and public stock mergers. In almost all cases, I would advise against the former. The latter can be a great boon or bust. It really depends on the deal.
Earnouts — Multiple books could be written on the structure of earnouts. They are one of the more complex consideration tools and also the tool fraught with the most manipulation and headaches. In order to be fair on both sides, they simply need proper structure.
Notes — Simple interest notes are most common and often allow a buyer to kick the can a bit on paying all cash up-front. It can also help the seller to spread tax burdens over several years.