Tokyo Babylon

Tokyo Babylon is what I call "anime without a net". In Japan, these sorts of OVA are supported by long running manga, and fans need little or no explanation of who the characters are or just what's going on. The problem with this, of course, is that the related properties are not necessarily available in other countries. In the case of Tokyo Babylon, people who stick almost exclusively to anime can glean more from X - but it took eight years to get that far.

Sumeragi Subaru is a medium. Occasionally he is hired by people to "psychically investigate" various cases, be they helping widows come to terms with their loss or, in the case of these OVAs, working with the police to assist with their inquries.
In the first episode, Subaru is asked to look into a curse and if it is possible that a man could be blessed with such luck that he could deliberately insert himself into life threatening situations, leaving all but him dead. In the second, Subaru is witness to a murder on a train. Involved in the case is a post-cognitive woman who can see the past through touch. Feeling sympathy for her, he can't help coming to know her personally as well as professionally.

Tokyo Babylon has interesting ideas, post-cognition in particular, but it suffers through a lack of any real context. Subaru lives by himself, but he frequently visits his friend Seishiro another psychic who doubles as a vet. His sister, Hokuto, doesn't live with him but is always at his house. She doesn't get up to much other than wearing some creative clothes.
Who are these characters and what are they doing here? This stuff is probably great for a pre-existing fan base, but well, it's a void for those not in the know.
Subaru is one of those weak characters who equates misplaced mercy with strength. Someone who has killed so many people over a ten year period does not deserve to be attacked less than wholeheartedly, yet Subaru refuses to cut loose. The real reason that Seishiro is included appears to be to bail Subaru out through his use of amazing cryptic powers. Again, this is material that might make more sense in the context of X - perhaps seeing Subaru optimistic and relatively happy is good for contrasting. Only time will tell in this case.

On reflection, the stories are told in a rather disjointed fashion - seemingly unrelated scenes are simply thrown in so that later on they can be tied to the main plot. While in mysteries it's expected to turn minor points into integral parts of the whole, here they're inserted with very little coherence. When scenes are just laid upon scenes, it seems more than a little lazy. The way that these scenes here were integrated was also a "spoiler", which although obvious ruined a lot of potential tension.
However the theories are sound, despite the backgrounds and characters they are painted upon being less well realised.

This is a fairly drab production. The music is sparse, and there is a truly horrible Engrish song by Matsuoka Yoshiaki. Two, in fact, but they sound so terribly alike that there's no way to distinguish between them. Matsuoka, in an amazing coup, wrote, composed and sang both Kiss Kiss and Strawberry Kiss Kiss. Whatever there is good about this anime is almost cancelled out by this train wreck of a song, way out of date in 1994.
Takahashi Kumiko converted the character designs for animation, but not as successfully as she did later for Cardcaptor Sakura. Subaru looks almost exactly the same as Hokuto and wears some highly questionable tight clothes. In the second episode, two other characters are nearly indistinguishable, which becomes quite confusing.
That said, Tokyo Babylon is not entirely without visual flair. The showdown between Subaru and Nagumo in the first episode has some innovative action ideas, and the second is definitely more polished. The colour scheme is fairly uninspired, however, and it's not as nice to watch as it could be.
Yamaguchi Kappei is uncharacteristically placid as Subaru, Takehito Koyasu his usual smooth self as Seishiro and Itou Miki loud and embarrassing (accurately so) as Hokuto.

Tokyo Babylon by itself is cryptic on a not quite impenetrable level. Watching X might shed some light on this as an interesting character study, but this anime is not recommended as stand-alone viewing.