Since I have already summed up most of my general feelings about the Persona 4 Social Link system, it is time to look at some of the individual Social Links in depth.
Culture Clubs: Much like in Persona 3, you get to choose one club to join for each of two categories, and these clubs have associated Social Links. The big difference here is that the choice in club actually matters. In Persona 3, whether you picked the Art Club, Music Club, or Photography Club, you were still going to end up in the same club as teammate Fuuka and Social Link character Keisuke, which certainly makes you wonder why they bothered to give you a choice at all. In Persona 4, though, choosing the Drama Club will open up a Social Link of the Sun Arcana with a girl named Yumi, and choosing to join the Band will open up a Link of the same Arcana with a different girl (I don't really know who she is, since I am still on my first playthrough). This means the choice in club may not have any significant gameplay difference (as far as I am aware), but it does change the subplots and scenes that you experience across the game, which adds to the game's replay value and makes the player's choices feel more important. This is certainly a nice improvement.
Sports Clubs: As with the culture clubs, the choice of which sport club you join is far more significant than it was in Persona 3. However, it implements that significance in a different way. Both club choices have an associated character, but regardless of which choice you make you will befriend both of them (since they are close friends with each other). Far from making the choice irrelevant, though, your choice in club has a major impact on the storyline associated with that Social Link. Thus, you meet two great characters either way, and there is still a significant difference based on the choice. Also, having larger groups of people hanging out with each other in Social Link scenes makes them more interesting and dynamic, which helps a bit. I actually like this implementation of the club choice better than the culture club variation.
The Fox: This is a truly bizarre and fun Social Link, that doesn't work quite like any other. For one, the fact that it is a Social Link with a surprisingly intelligent animal that can't talk is strange enough, but but even more strangely it doesn't even use the same system to determine its growth as other Social Links. Rather than build up affection with the Fox, you must solve people's problems with the game's quest system in order to unlock higher levels of this Social Link. What is more, the Fox actually goes with you into the game's dungeons and provides special healing services there (and building the Social Link gives you a discount on those services). The unique way you build the Fox up makes it stand out as a refreshing change compared to other Social Links, and its added usefulness makes me wish that more Social Links were given side benefits and a role in the game's dungeons.
Margaret: This woman is another strange Social Link like the Fox. She is the assistant to Igor, the strange figure that fuses demons and Personas for the heroes in pretty much every Shin Megami Tensei game, and thus doesn't even really exist outside of the mysterious Velvet Room that only the hero can visit. As such, raising her Social Link is based around bringing her unusual Personas (this makes it a lot like the Fox), and doesn't even cause time to pass. The fact that there was no Social Link with Elizabeth, Igor's assistant in Persona 3, always seemed a bit strange (particularly in FES, where you can go on dates with her), so this is a nice touch. This unusual Link also adds some much needed variety to the game, and helps add to the number of plot important characters who have Social Links (a nice trend in Persona 4 that needs to be carried even farther).
The Dojima Family: Both the hero's uncle and cousin are Social Links in this game, and they are easily two of my favorite Social Links in the entire game. The simple fact that the game's nameless hero actually has a family is nice enough in of itself, but just as important is the fact that these are the only Social Links other than the ally links that are with plot-important characters with a large number of voiced lines of dialogue. As such, the Social Link scenes don't have to bear the entire burden of developing these characters and portraying the hero's interactions with them, and they appear frequently even if you never build up their Social Links. This means that, even though their Social Link scenes are dominated by central problems (in fact, both Social Links share the same problem, just with two different sides), these problems don't create the same issues to anywhere near the same extent that they do in other Social Links. Other than the ally characters, these are the only two Social Link characters who react to the game's plot and have an impact upon the greater story of the game. The Social Link system would really benefit by making more Social Links resemble the ones with the Dojimas.
None of the other Social Links are really notable enough to be worth mentioning, so I may as well wrap this up. I still need to write more about ally Social Links, but that is going to be its own post, and I need to play a bit more of the game first. I may need to shake off the grip The World Ends With You has over me before that can happen, though...