Aside from the obvious things like GTS trading is there something in the games you can't get anymore after
Wi-Fi Connection is shut down? I remember that you could only get some medals in BW2 if you connect with the internet
but not getting some medals isn't the end, but is there more?
Well, it is very much contingent upon the generation/ games that you're most concerned with (or that you have). If you haven't been playing Pokemon for too long, then in both Generations 4 and 5 there are a number of event or other legendaries needed to unlock special in-game features, including storyline events and similar items of interest. Most of these Pokemon will be essentially unobtainable when the Wi-Fi goes down. Please refer to my first post in this thread for more information about these Pokemon. If you're one for completing the Pokedex, there are additionally a pool of version exclusives one needs to worry about obtaining. You might also want to pick up a Japanese Ditto or two from the GTS in order to try your hand at Masuda Method breeding.
In Generation 5, the situation is a bit more complicated. You have the aforementioned event legendaries, but there are also a large number of Berries and Hidden Ability Pokemon to worry about. Some of the latter are newly catchable in Black 2 and White 2, but, in light of the closure of the Dream World, many more are only available via trade. The event Berries (Custap, Jaboca, Rowap, and Micle) can now only be traded for too. Basically, it all boils down to what exactly you like to collect.