Random is King in Amber, and has been for twenty-five years. He's doing a good job so far; his wild nature seems to have mellowed, and he's sharp enough that the corruption and the sinecures have mostly vanished from his government. Gerard backs him strongly, and so did Bleys; there have been no attempts to seize the throne.
Benedict has been reclusive of late, and perhaps spends more time in Shadow than in Amber. It is rumored that one of his loves died birthing a child, but few have dared to search out the truth.
Flora and Random don't really get along, but she has supported his place on the throne throughout. After she warned him of an assassination plot last year, there have been hints that she will be allowed a greater role in the court.
Caine nominally shares Gerard's governance of the Navy, but his allegiance to his ships seems to have faded. He spends much of his time in Amber.
Although Brand never returned from the Abyss, Deirdre _did_ eventually return to Amber, explaining that she was 'caught within the Jewel' when the Unicorn brought it back from nothingness. She spends much of her time in artistic expression, and is currently working on a thirty foot long tapestry, in brilliant colors. She keeps tabs on the kids and even on the elders around; she'll usually do a favor if asked. She has a daughter, Penelope (aka Marya), who was presented in the Great Hall on Fiveyears' Night.
Bleys, on the other hand, reprised an earlier role and fell off of Kolvir a second time. Fiona, who basically controls the Amber judicial system, has not announced any evidence of foul play, although it seems likely.
Llewella has returned to Amber at Random's strongly-phrased request. She doesn't talk much; nor does Julian, protector of Arden. Julian has one daughter, Caity Schorr, an abject failure. He only recently acknowledged her at all.
Corwin ... well. He returned at Fiveyears' Night, to many people's sorrow.
Several others may be a part of the family. It seems fairly certain that Deanor is indeed Brand's son; Valerian has claimed to be Eric's child; Camille has walked the Pattern, but will not discuss her parentage; finally, Phillipe was found at the center of Corwin's Pattern, so ...
There is more information available on Patterns.
Shavings of True Stone