Sonic Shipping, Logically Speaking; SilverXEspio
Time to get the posts of context out.
Characters involved: Silver the Hedgehog and Espio the Chameleon.
Most well known nickname: Espilver? Is there one?
Original date of ship: 2007
Analysis of chemistry (aka why people do/don't ship it): It's really based on one game, Sonic Rivals 2. In it, Silver comes to the present time to find and stop Eggman Nega. He does this by taking Chao to make sure Nega can't find them and feed them to Ifrit. This inevitably gets noticed by people, and the Chaotix are eventually called to investigate. Espio eventually finds Silver, and Silver slowly explains the Ifrit deal, where the two work together to approach Nega and stop him. By the end, they're on good terms, but Espio doesn't have the gall to talk back to Vector when it turns out that he hadn't explained any of this to him, and ditches Silver to run away from the transmitter. In story, nothing really there, but it's certainly better than Silvamy.
In terms of personality, there isn't much to say. They're kind of similar (although Silver could be said to have been more brash than normal anyway), and Espio gets to talk to someone that isn't in the Chaotix. Nice? Although, unlike the friendship between Sonic and Tails, it isn't close enough that they wouldn't want to fight other if needed (as seen by the multiplayer requirements).
Personal Opinion: Neutral buuuut there's a couple I like way, way more.
Likelihood in the games: Oh dear.
If Sonic Rivals 2 somehow stays in canon, it's still very unlikely. Even considering that Silver is borderline for prominence so he could maybe possibly get away with a homosexual pairing, they haven't really spoken since then, making it seem like it was intended as a one-time partnership like Amy and Silver were in Sonic 06.
However, Mario and London Wii poses a whole different problem. Through Silver's dialogue in party mode, Sega appears to consider Silver as not knowing about chameleons and how they can go invisible (it also rendered Vector playing the keyboard/DJing as non-canon, for another example). This is in direct contradiction with Sonic Rivals 2 where he would, and did, know about these things. As long as these little tidbits are consistent with Sega's thought processes, as well as the things pointed out in the relevant post of context, then the possibility goes down to zero because they haven't met in the way they did then and thus don't know each other beyond a very basic level. Man, Silver gets all the jilting.