Dr. Arthur Thurmond
In "The Quarantine" he has a heart attack, and then is never mentioned again... except for a little snippet at the end of "The Great White Hope" when Phillip unwraps a Christmas present from Thurmons
Dr. Geri Infante
She testified against Geiger and was never mentioned again.
Billy's Father
At the end of season three Billy tries to kill his father. His father is then brought into the hospital, the season ends, and nothing is mentioned.
Dennis's Sexuality
During season two Dennis and Camille flirt a little, he mentions that he used to live with a white female. Then during season four Dennis tells Aaron that he is gay and nothing is mentioned again.
Hospital Councel
During the first season Alan Birch was the hospital's lawyer. After his death the hospital went through a series of lawyers and then they were dropped. During the 5th season a lawyer turns up out of the blue, but we don't know yet who he is or if he will return.
Karen Wilder
She's a physical therapist at the hospital. An old friend of Jack McNeil and has dated both him and Aaron. Dr. Lisa Catera joined the hospital staff and Karen was never seen or heard of again.
Maricella Kieth
A nurse at the hospital, with an eclectic look. She takes an interest in Aaron, they kiss, possibly sleep together, and then she disappears.
Gordy, Billy's dog
He was in Billy's apartment when it caught on fire. In "Divided Loyalty" Billy blames Gordy for the noise from the living room, but he isn't seen. And then Gordy just disappears..
UPDATE: Gordy has been brought back into the show. We don't know where he has been for the past few years but in "A Goy and His Dog" Gordy was brought back into the storyline.
Bam Bam biting Diane
Diane successfully transferred the HIV virus into Bam Bam, a monkey. Then he bit her, and broke skin. But the story was completely dropped, we can assume that she would check for the virus after getting pregnant but it was never mentioned.
Diane's adoptive parents
Are they alive, dead, what? We know she's adopted. Her father received a transplant at one point. Billy has stated that she is an orphan. But it's never been mentioned what happened.
Danny's manslaughter arrest
Danny was arrested for manslaughter after a patient died. He was released on bail and was not allowed to operate on patients. Then he said he was going to quit and nothing was ever mentioned on the case.
Kate's Diabetes
It was revealed in the second season that Kate had diabetes, this was discovered during her pregnancy with Sara. It was mentioned once during the third season and has not brought up again. This should come into play in the Kate in Space story line that is happening now, but it hasn't yet.
The Puddle
This was once a favorite hang-out of the staff. They were always gathering at their favorite bar for a drink.
The Mummy
Diane was working to cure virus's from an Egyptian mummy. Did she grow them, did it not work? Who knows?
Aaron's Couch
Aaron was obsessed with his couch, well more importantly who was having sex on his couch. And who was? Will we ever find out?
Kate's Quitting
Kate quit the hospital at the end of season 3. During the first few episodes in season 4 reasons were given as to why Kate was still at the hospital and then it was dropped. We were never given a reason why Kate never left.
Aaron's father
First his father died. Then we find out that his dead father wasn't his real father. Aaron was the result of a love affair between his mother and a sculptor, Zoltan Carpathian. And his father has never been mentioned again.
Camille's Life after she left the hospital
In "Brain Salad Surgery" we are told that Camille is married and has two kids. In "One Hundred and One Damnations" Camille says that she isn't married and that she was just kidding before.
Kronk's Hockey Playing
Billy used to play hockey all the time, and would talk about it often. Now it is never mentioned.
The Interns
During the third season a group of interns were introduced to the hospital setting. They were around for a little while, one quite and then they all dissappeared.
Jake Luft
He was the man that had Diane's heart before Billy. He came around the hospital a couple of time and then just disappeared, did he go back to Africa or what?
Ricky Jackson
Danny and Billy help him with his make shift clinic that he ran out of his home. Kieth caught Danny giving him a box of meds, then Danny goes ahead and gives the medicine and supplies to Ricky (even though Kieth forbid it) and Ricky is never heard or scene from again.