The most remarkable aspect of geth culture is that it may not exist at all. Geth are a network intelligence; a single entity in myriad bodies. They share data with one another, whether discrete facts or "memories": audiovisual recordings of experiences and logs of thought-processes. Any event experienced by one geth is uploaded to the group mind, so that all geth, everywhere, "remember" such an event as if they'd experienced it themselves.
No one knows whether the geth develop personalities as organic-created AIs do. If an organic-designed AI is transferred into another quantum bluebox, its personality is reset. Most geth programs transfer from one hardware platform to another constantly; if a geth needs to travel to another star, it downloads into a starship body. If it needs to replace a piece of malfunctioning hardware, it downloads into a small body with hands. If geth are reset at transfer, it would make development of individual personalities unlikely.
Records of the quarian war suggest the geth have no concept of self-preservation. They do not flinch from gunfire, and do not hesitate to sacrifice themselves if it allows their fellows an advantage. Thousands of mobile platforms were expended assaulting quarian positions, but file-sharing between platforms ensured their memories and experience would not be lost. Geth are therefore immortal; if their hardware is destroyed, archival copies of their programs and databases can be downloaded into a new body.
With the gap in contact between the quarian war and the arrival of Sovereign, the only proven fact about the geth is that they were isolationists for centuries. They never ventured outside the Perseus Veil, but no organic ship that entered their territory ever returned.