Auto incremented numbers can be so nice for unique IDs in a database; they're guaranteed to be unique, can range to fit your needs (tinyint to unsigned bigint), and easy to use. When working in a sharded environment, they may not fit the bill anymore; you either lose global uniqueness or you lose ease of use (depending on your sharding mechanism). One very good alternative is to use UUIDs.
UUIDs solve the global uniqueness and ease of use problem at the same time, but introduces another problem in the database layer - memory footprint. A UUID is a 36 byte ASCII string of characters representing a 16 byte value. I've seen them stored as CHAR(36), VARCHAR(36), etc. The problem with storing them in their ASCII form is that the index will grow beyond the capacity of the database server faster than when they're stored in a binary form. Memory will fill faster, queries will hit the disk more frequently, and it will ultimately cost more money to save the exact same information. It's not worth it.