Virtual Eugenics

One of my disappointments about the continued normalization of Stardock's Elemental was the removal of the royal marriage and lineage system. Granted, in the original incarnation of Elemental the system was only rudimentary, but that was to be expected. Not only was it one small part of a larger, ambitiously multifaceted project, but it's a feature that's so conspicuously absent from RPGs (not to mention TBS) that it was largely a wild card. It could not be copycatted from a popular competitor. Its potential effects on gameplay were far-reaching and difficult to predict.

And that's good. That's what creativity looks like from the outside. Shit like you've never seen! Yes, it might turn out to be frustrating, but guess what: so are dice, and they have been for forty years and before that for... umm, how many centuries old is backgammon again?

As far as having in-game characters breed, my main concern is not with the role-playing side of things (pornographic or not) but with the strategic options this would open up.  I'm sure many tabletop RPG systems have incorporated something like this, but as I have no experience with the top of tables, keep in mind I am talking about games situated at top-of-desk.

Lineages should work very well in single-player strategy games with a roleplaying component if the player is not asked to transfer himself into a new body, if the player is immortal, the founder of a clan into which outsiders marry and the offspring of which inherit various traits. It's another way of customizing one's army.
Before you scoff at the ridiculousness of this, allow me to cite precedent. If Elrond can have his great-to-the-grand nephew Aragorn fighting his battles for him, why can't I? (Numenor's kings and their descendants in Arnor and Gondor were descended from Elrond's brother, Elros.)
That seems what Elemental was trying to set up initially, and it has great potential. Breed a clan of frost-magicians one game, or chase mates around the jungle next time to sire a line of voodoo priests.

In multiplayer, things get more complicated. Sheer roleplaying takes a back seat to balance and the challenges of implementation in a system of player interaction.

Let's start with the basic idea of claims to the throne. This can only really work in single-player (see Europa Universalis 3) because multiplayer games devolve to pure favor-currying anyway. There is no plausible mechanic to force players to adhere to the strength of a blood claim. There's no way you're going to get players to support you, the son of the defunct king, over your thrice-removed cousin who happens to be their real-life buddy.

There's a bit more potential in a hard-coded division of material resources.
Say you marry your pal Bob (a.k.a. Roberta Frostpoke the elven archer with gigantic knockers and a +5 battle corset) and you at some point kick the enchanted bucket and not even an affectionate, hammy "why, gods, why" grieving scene from Roberta can revive you. You reincarnate yourself into one of your five children. Does the new you at that point instantly get all the old you's possessions? Or does something automatically go to your four siblings who are presumably living comfortable lives as NPC shepherds and one of whom Roberta will likely want to "Morella" herself into at some later date?
How do you limit players' breeding? Make a bit of all the money they get go to support their NPC offspring automatically? Make "vasectomize" a cleric spell? Go all-out and train a bunch of rogues with "greater weapon focus: pruning shears"? Do you code in legally-binding wills in which players state who gets their unicorn mount on death, or give up and assume they'd cheat their way out of it anyway?
Should fantasy weapons, which are generally immortal, become bound to a particular bloodline? Is Anduril only a threat to Sauron if wielded by a descendent of Isildur?
In scifi games, does the galactic bank hold precise records of inheritance, replacing part of players' ability to trade goods? Can Arrakis only be managed and mined by an Atreides / Harkonnen unless you kill them off?

Much of this has to do with the most interesting facet of the issue, genetics. How likely should the above-mentioned couple's offspring be to inherit Roberta's deadly, deadly corset-magic abilities, and how much will you be allowed to determine just as you would when creating a new character normally? You can see this as a more narrowly-focused version of racial characteristics.
Should you be able to offer other players "incarnation rights" to your ever-so-gifted offspring (for a reasonable sum) or will reincarnation be limited to direct descent?
Should characters inherit genetic weaknesses as well, to counteract the benefit of inbreeding to select for perfect corset control?

What about controlling the breeding of NPC populations, humanoid or not? True persistent world games tend to feature a good deal of automation to compensate for players' offline time. This can be handled by NPCs and in a game with a lineage system, you and Roberta can have your mithril mine and fig farm staffed entirely by your NPC offspring. It might ensure they won't cook the books and sell you out to the goblin mafia, but you lose out a bit because they keep taking the magic carpet out for joy-rides.
Or how about breeding the perfect war-horse? Maybe you want one with pegasus-blood, or a half-unicorn.
Maybe you sire a few illegitimate offspring with your NPC mine workers and a few generations later other players are paying your clan for the privilege of hiring workers off your lands because they're resistant to corset hypnosis.

The possibilities, as with divine spellcasting, seem endless. I won't even get into the issue of inheriting cross-racial abilities a la DnD dragon disciples.