I acknowledge that wikipedia defines a soap opera in that manner. However, i would submit that to do so defines the genre so broadly as to be a definition without meaning, at least in the modern age of television (where dramas are no longer required to reset to the status quo at the end of every hour).
Off the top of my head, that definition means the following television shows, all of which were ongoing, episodic and somewhat serialized (insofar as they had recurring plots that carried over from week to week until concluded), were/are all soap operas:
- Hill St. Blues
L.A. Law
ER
Lost
the Sopranos
Deadwood
the Shield
Justified
the Wire
NYPD Blue
House
Alias
24
the West Wing
Breaking Bad
Fringe
Buffy
Dexter
And that's just drama shows, the same definition, if applied to comedy would mean the following are also soap operas:
- Seinfeld
Friends
Curb your Enthusiasm
the Venture Brothers
the Office (US and UK versions)
30 Rock
HIMYM
Furthermore, you can't really use the "other subgenre" distinction because there have, in fact, been soap operas that were steeped in, for example, medicine, police drama and the supernatural (Dark Shadows being the obvious example).