Reasons

So why a shrine to these two individuals? Well, why not? In the RK fandom, there is a sad lack of Megumi/Aoshi shrines yet a growing cadre of very good fanfics out there that explore this particular pair. However, aside from that --

Watsuki, beloved mangaka of Rurouni Kenshin, also apparently received a lot of comments about Aoshi and Megumi. To quote the Viz translation of the Megumi profile ("Secret Life of Characters") two main opinions prevail: 1> "Megumi and Aoshi are suited for each other" and 2>"Megumi and Sano are suited for each other." Watsuki's though was that perhaps the former preferred how Aoshi and Megumi were intellectually compatible and the others liked the fighting/chemistry between Megumi and Sanosuke. However, despite his readers' feelings he left things oddly unresolved at the end of the manga regarding the second pairing.

This site obviously reflects the preference towards reader opinion #1. Why?

They look damn good together. Visually they are complementary, even striking. (See manga scans in Images. Intentional or not, the two are always drawn in counterpoint. They balance one another in a picture.)

They have a unique chemistry -- one that doesn't involve screaming or beating each other up, or pure adulation. They treat one another as equals, as adults.

"They are more compatible intellectually and in terms of maturity. Plus, if you think about their pasts, they've shared some parallel experiances: both lost their families (her blood-relatives, in Meg's case, and Aoshi's men in his); both hide their true feelings behind facades (Meg a flirtatous persona, Aoshi behind a cold face), both seem to feel like outsiders in their new 'families', eventhough they know that their friends care deeply for them. They would probably be able to understand each other well because of the similarities, and communication is the key to a good relationship ;) And in the Jinchuu/Revenge Arc of the manga, it's shown that they can work
together, despite their past history." [Ann _ ]

Their personalities complement one another well. Megumi stands up to Aoshi several times over the RK storyline. But on the flip side, he can also tame her and reason with her - as demonstrated in the Jinchuu arc.

Their lifestyle goals are also compatible: At the end of the RK storyline, we see that she desires for a more settled life in Aizu - where she continues to heal and seek out her family. Aoshi too pursues a quieter life; leaving behind his fighting and seeking out focus through meditation. Contrast these two with a young, flighty Misao and the absent, wild Sano, and you see that these two are a more sensible pairing.

CherieDee -- one of the earliest fanfic writers for this pairing mentioned specifically that "One of the reasons I really like writing the two is because the subtlety involved. They're both people who understand that feelings don't necessarily have to be expressed through words, but through action...."

In more recent discussions, I think there are some interesting differences we've noted about this fandom. You might wish to read Shimizu HItomi's rather length discussion at her site or the dissection by eriesalia here, but there is an attraction to the psychological survival motif of both Aoshi and Megumi as well as something a bit incomplete to their encounters. What is interesting is that these two are adults that are complex and in spite of their history demonstrate a certain willingness to work together. It is a bit unfortunate that the Jinchuu arc did not get animated faithfully and in detail (other than its inclusion in Sessouhen), as it goes counter to season 3 in showing these two together, functional.. not quite whole, but on their way there.