In the beginning of the series, Ziggy is very detached from everyone in the party. It isn't until around the encephalon in Episode I that he starts to really interact with the other characters, minus MOMO of course. Here's a rundown of the major interactions within the game.
MOMO - (More Information)
The 100-series prototype is the one character to share the closest relationship with Ziggy. They are quite an unlikely pair. MOMO longs to become fully human, while Ziggy wants nothing more than to erase his humanity and become a machine. Furthermore, MOMO often reminds Ziggy of the life he had before being revived as a cyborg. She becomes a constant reminder of his remaining humanity. At the same time, Ziggy provides guidance and support that a father figure would for his own child. Sometimes it seems as if Ziggy takes MOMO under his wing. However, I think their bond cannot just be defined as friend or adoptive father and daughter. I sometimes imagine it to be more of a combination of both close friendship and a sort of familial bond. Because of this, the relationship between these two characters is extremely dynamic and interesting.
Ziggy sees a lot in Junior that he also sees in himself, or rather, how he used to be. I also believe that Junior reminds him of his step-son in a few small ways. However, I think he is merely trying his best to look out for him. He doesn't seem to take well to Junior snapping at both him and MOMO in the KOS-MOS encephalon. When MOMO is captured by Albedo, he says that he's going to go after her alone. However, Junior wants to come along. Ziggy tells Junior that he shouldn't go because he knows that Junior won't be able to control his emotions in the situation. Ziggy tells him that he's seen the results of that situation happen too many times, trying to pass it off as merely observing. However, he was talking about seeing his family die right before his eyes. He didn't want Junior to go through a similar situation, and face the same kind of pain. The speech that he gives him is more like his way of telling him that he actually does care, despite his cold and detached outward appearance. Junior doesn't seem to pick up on this, and reacts harshly to him. Afterwards, he refers to Ziggy as "Old Man", but over time it grows into a more affectionate term of sorts. Eventually, Junior learns to appreciate Ziggy's wisdom. Likewise, Ziggy cheers him on before going to the Space-Time Anomaly to stop Albedo. At the end of Episode III, Junior asks Ziggy to take care of MOMO and Juli for him, passing on the promise he made to Sakura. I think this shows the amount of trust that the two of them share.
MOMO is registered as Juli's legal daughter. However, at the beginning of the series, she regards her as more of an object. Ziggy realizes this from the start, but he doesn't bother to question her about this behavior until Episode II. He asks Juli to consider MOMO as another child instead of a copy of her late daughter, Sakura. Juli realizes that this is a tough challenge. Not too long after, Ziggy pleads with her not to terminate her systems in order to keep the Y-Data from reaching the wrong hands. However, much to their surprize, MOMO did this herself, and both Juli and Ziggy run to her side. After the whole ordeal, MOMO begins to grow on Juli and she asks that Ziggy remain alive just a little longer for both of them. Because of Ziggy's words, she begins to treat MOMO as another daughter. By the time we see her again in Episode III, she is a different person. At the end of the series, Ziggy lives nearby (or with) them on the Dammerung, helping to build a new network with Scientia.
Erich Weber / Voyager
Erich Weber was a subordinate of Jan's during the time when he was human. His main job was to provide support to those diving into the UMN. The whole time, Jan had been investigating who they thought to be a cold-blooded murderer. However, he never expected it to be someone he had worked so closely with. In order to fufill his contract with U-DO, he took the lives of Sharon and Joaquin, his wife and stepson. Afterwards, he offered Jan to join him as a Testament, or continue to live inside his brain with his departed family. He refused and killed himself. He doesn't encounter Voyager again until the end of Episode II. At which point, he tries to attack him. However, Voyager sends his attack back at him. During Episode III, Ziggy can do absolutely nothing to him. It turns out that Canaan is the only one who is able to stop him. After Voyager is finally gone, Ziggy finally is able to find peace.
Shion seems to depend on Ziggy a lot for his strength, and also his wisdom throughout the series. He seems to always be there to help her. At the end of Episode I, he stayed behind in the basement of the Elsa to make sure that Shion would be all right. When Shion looses her grip on KOS-MOS, Ziggy reaches down and grabs the android just in time. In Episode II, they don't have as many interactions. This is namely because the game focuses on MOMO, Jr. and Albedo. However in Episode III, we get to see a better glimpse at Shion's dependancy on him. When she realizes that she called the Gnosis into the universe fourteen years ago, she runs from Jin (and passes Allen, go figure) and goes to Ziggy asking if it's really true. Ziggy just stands there not knowing what to say. However, earlier in the game, she asks if Junior is all right, even though Ziggy was just tossed across the room by Voyager. I suppose she cares about Junior's well-being more than Ziggy. At the end, as the Elsa is flying from Michtam escaping the growing void, Ziggy is there holding Shion and Junior up. I think that he sees Shion's reckless nature. Perhaps in a way, it reminds him of how he used to be (and how he becomes when he allows his emotions to surface). So, he feels the need to watch and make sure she doesn't do anything too stupid.
For the most part of the series, Canaan and Ziggy have little to no interactions. However, their relationship is quite signifigant. It is revealed that Canaan carries the same personality of Lactis, an early-model Realian that worked on Jan's team during the Voyager investigation. When Ziggy realizes this, he's suprized and shocked. However, he doesn't have a chance to form any sort of bond with him. After fighting with Voyager, and realizing how powerless he is to do anything, Canaan comes to their rescue, calling him "Captian". He tricks Voyager into trying to attain power from the Compass of Order. Although Ziggy rarely shows much emotion, he is cleary upset by this, and begs him to stop. But Canaan refuses. Then, as Voyager dissapears along with him, he says that he doesn't want to exist just to see him die. Instead of betraying everyone, he wanted to help them. After he's gone, Ziggy says, "So you chose the same path I did, Lactis."
KOS-MOS and Ziggy don't have many signifigant interactions during the course of the series. However, Ziggy is responsible for saving KOS-MOS during the escape from Proto Merkabah. When Shion loses her grip on KOS-MOS's hand, Ziggy reaches out and grabs her, pulling her in. Also of note, KOS-MOS and Ziggy are both the strongest physical fighters with the largest HP by default, at least in Episode I. During Episode III, she return the favor and catches him after T-elos effortlessly fiings him in the air and kicks him.
Out of all of the main party members, Ziggy and Jin have the least amount of interactions. The only time that they really do interact in the course of the game is during Episode III. If you wander around the Elsa before going out to Old Miltia with Allen, you'll find Ziggy and Jin engrossed in conversation in the weapon room. I would think that Ziggy and Jin have a kind of understanding, since they're both the oldest (save for chaos), and they both take on protective roles for other characters in the game. At times, Jin can even been seen guarding MOMO and trying to be supportive of her. When Jin leaves everyone in E.S. Asher for the last time, Ziggy is the last one to join the rest of the group at the edge. Although, I would imagine that he's feeling the same way everyone else is about him leaving.
Although chaos and Ziggy don't interact very much in the games, chaos did play a rather big deciding role in Ziggy's past. While diving into the consciousness of a man who they thought was Voyager, Jan collapses and sees bits and pieces of his past. At one point, he chases one of his memories. Then, a mysterious voice speaks to him. The picture that accompanies the voice in the game is a blurred version of chaos's character art from Episode I. Here is the dialogue they exchange at this point.
chaos: Waiting beyond that shadow is the eternal prison of the soul. That is... a cold death. Your memories will not give you peace. You should know... There are people that you must protect...
Jan: People I must protect? As a policeman I protect the public order...
chaos: No. Special people you must protectÉ not as a policeman, but as you yourself. ...Also, the place where you are now is not a world that needs you. It is...
In Episode II, he seems to have referenced this peticular bit of dialogue. However, due to the fan translation of Pied Piper and the official translation to english in Episode II, we get something sort of similar:
Ziggy: Death is rest for the soul. Who was it who said that? If the body did not die, and the fears borne in the mind just continued to pile up, the world would be nothing more than an eternal prison.
Following Ziggy's remark, KOS-MOS turns towards him and nods. I find this very curious due to who is really hiding inside the android! We don't see chaos at all during his speech because he's standing behind him. Could KOS-MOS be reacting to chaos' thoughts and emotions similar to the way she did in several instances in Episode I?
Wilhelm makes a comment on chaos's interference with Jan:
Wilhelm: ...Yeshua. Going so far as to get help from others to obstruct me isn't like you... Still, if that's what you intend to do, I too have something in mindÉ While you hide in the shadows, I will see to it that things get done my way. ...But I am content to wait... for the day when you will once again return to the stage...