First, I'm going to state that all charage/moege are harem-ge (with the exception of kinetic novels with only a single heroine). In all these cases, you have a bevy of heroines that are, at the very least, friendly with or somehow attached to the protagonist. There are a three standard types of harem that I consider to be general umbrella types. These harems do not include nukige sex-only harems or the type of harems that pop up in gameplay hybrid VNs, as these often have distinctive story-exclusive reasons for harem formation.
The Disconnected Harem
This is the standard-issue harem for modern charage/moege. In this harem situation, the protagonist is independently connected to most of the heroines, with very little or no interaction between the members of his harem of latent deredere troopers. The reason this has become the dominant harem in the charage genre in the last seven years or so is because it is the one that is the most 'tasteful' to monogamists and traditionalists. In this case, the heroines either have no real connection with one another or only weak connections that become tenuous the second the heroine path begins. Games that have these harems tend to have extremely weak casts of characters in general, and there is usually very little or no real conflict between the characters (low incidence of love triangles, few jealousy attacks, etc). As a result, games with this type of harem tend to have weak or nonexistent plots, lackluster SOL outside of ichaicha dating, and 'convenient' drama that is resolved so quickly it might as well not even exist. These harems generally disband at the end of the common route, as the protagonist seems to completely forget any attraction he had to the other girls and they fade into the background.
The Dominant-Sharing Harem
The Dominant-sharing Harem is defined by the members of the harem being at least somewhat familiar with each other (often friends, family, or members of a group or club) and able to be cooperative to an extent while competing for the protagonist's love and attention. Girls in this kind of harem situation (Shuffle is a prime example of it) are ok with the idea of sharing the protagonist in the abstract, but in practice they want to be the 'first wife' or the 'wife' and relegate the other heroines to the mistress or concubine status (though it isn't always stated this bluntly). This is perhaps the most realistic harem situation, as, historically, real harems - other than royal ones - have usually been structured with a head or first wife and a number of secondary wives, often married with the permission of or by the choice of the first wife, lol.
The Everybody's Equal Harem
The Everybody's Equal Harem is, just as the name indicates, a harem where the protagonist essentially loves and treats all the heroines equally and the heroines accept this situation, albeit often with a tacit understanding between one another that they won't stop aiming for a Dominant-Sharing type situation. As such, this can often be considered a prelude to a Dominant-Sharing Harem result in practical terms. A classic example of this would be the end of the Grisaia series or the ending of Strawberry Feels, where the protagonist himself never forms a preference, even if the heroines do build a sort of pecking order based on dominance of personality or circumstance. Tiny Dungeon's Endless Dungeon ending can also be considered this kind of ending, whereas the individual routes represented by the first three games would be considered Dominant-Sharing harems.
Why I bothered with this post
Anyone who has been an otaku as long as I have been has to accept that harem-thinking is essential to SOL otaku-ism. As early as Love Hina and Tenchi Muyo, rom-coms have been creating wacky harems and weird situations that result. This is because romantic comedy is the easiest type of comedy for anyone to get into, and the easiest one to empathize with... and comedy used to be the dominant genre in otaku media (though romance always came a close second).
The evolution from that type of loose harem (though in later incarnations, the Tenchi universe threw off all pretense of not being harem-ist) to the current situation took decades, but it was a natural evolution in visual novels in particular, due to the fact that most visual novels are multi-route, heroine-focused affairs. Charage in particular, with their focus on SOL, inevitably give off a sense that the protagonist is the center of a harem, even if it is only in the common route. Since this kind of situation appeals to the more primitive parts of the male psyche (males are genetically predisposed to seeking multiple mates, though socialization and emotional attachment overwhelm this in modern settings), eroge tend to abuse this flagrantly.
Oh yeah, if you haven't figured it out, I like harem endings that aren't sex-heavy... but that isn't so much because I have a thing for 'collecting' bishoujos. Rather, I like the various situations that result in VNs, as they are often intellectually interesting, heart-warming, or hilarious (or all three). Nukige-style harem endings are boring and make me roll my eyes, mostly because I question whether anyone has that kind of stamina, and because ignoring the emotional and practical aspects entirely like that makes it hard to suspend disbelief. If a plotge can make me think a harem would work, I want to see it work, lol.