Ghosts

''"Seems like some poor blighters have started seeing ghosts. Ghosts! Ryan tells me it's a side effect of this Plasmid business. One poor sod's memories getting passed on to another through genetic sampling. Leaks. Lunatics. Rebellion. And now bleeding ghosts. Ain't life in Rapture grand?" - Bill McDonagh''

Ghosts are the leftover memories caused by a crossover of genes during genetic sampling, possibly because of recycled ADAM from Little Sisters.

Ghosts feature prominently in the story of BioShock, and are sometimes equally important as Audio Diaries. They are also a way of displaying to the player the exact repercussions caused by excessive use of Adam.

Transcripts
''"I'm... I'm too spliced up, I'm too spliced up! No one's going to want me!" - Female Ghost, Bathrooms in Welcome to Rapture.''

''"You don't fuck with Fontaine... Fontaine fucks you!" - 2 Male Ghosts, Roaming in Neptune's Bounty.''

Trivia
Ghosts appear to be the cause of passing Genes via re-used Adam. However, if Bill McDonagh's Diary was recorded before the Civil War, then the Little Sisters would not have been in effect yet.