The title creatures of Persona 3, the Personas, are certainly an important part of the game. Acquiring them, building them up, and fusing them together to create new Personas are all activities that take up quite a lot of time and energy. Almost every choice made in the progress of the game is reflected by the incredible variability of the Persona system. This system, the Persona series' inheritance from the broader Megami Tensei series, is essential to the experience of the game. In many ways, Persona 3's adherence to the traditional Megami Tensei system is both a great strength and a great weakness for the game.
The basic scheme of the Persona/Megami Tensei system is very similar to monster-collection games, though a bit less so in Persona than in the main Megami Tensei series because Personas don't fight directly and you can't build teams of them. One of the biggest differences, though, is that unlike more typical monster collection games such as Pokemon, the Megami Tensei makes holding on to your "monsters" and raising their level a less-than-optimal choice. Personas level at about half the rate that the hero does even if you put all of your effort into raising their levels, and raising the hero's level lets you acquire even more powerful Personas who have even stronger abilities, so it is most beneficial to use low-level Personas for fusion than to try to level them up. This means that the player will only use any particular Persona for a very limited time, and there is a clear progression of ever-stronger Personas. In many ways, it is a far simpler system for the player to use than other kinds of monster collection game because the basic choice of what monster to use is so much more clear. It is particularly good for a game like Persona 3 in which the "monsters" do not take center stage, because it makes it a lot easier for the player to make use of a great variety of "monsters" without having to spend a lot of effort acquiring them and individually raising their levels. Because of this, the basic system works very well for Persona 3, though there are flaws in the details.
One of the most noticeable flaws of the system is actually in the designs of the different Personas. In that area, Persona 3 may have taken a bit too much from the greater Megami Tensei series. All of the Personas used by your allies and enemies in Persona 3, from Junpei's Hermes to Aigis's Athena, all have a really great unified look to them, mixing human-like forms with surreal elements to create creatures that look like they are subconscious echos of the Persona-users, and they quite nicely incorporate a lot of the same design elements seen in the enemy Shadows (some Shadows, like The Reaper and some of the Twelve Shadows would actually make great Personas themselves), but the problem is that only three out of more than a hundred and seventy Personas available to the hero use that look (Orpheus, Thanatos, and Messiah). The rest of the hero's Personas all take their designs (and possibly models) directly from other Persona games, and don't look like anything else in Persona 3. I suppose the fair way to interpret this is that the designers wanted to keep the looks of the creatures the same between all Megami Tensei games for brand reasons (the unfair interpretation is that they were just lazy), but I don't think it was the best choice. The difference is just too glaring.
Another flaw is actually related to the three Personas that actually do match the rest of the game's aesthetics. These three, the hero's first Persona "Orpheus", the plot-central Persona "Thanatos", and the ultimate Persona "Messiah", are all among the most important Personas in the game, but in the end they are treated just like any other Persona. Orpheus is incredibly weak and should be abandoned quickly, Thanatos is just another Persona who will be acquired and traded out eventually (despite his important symbolic role in the game's plot), and as far as I am aware Messiah is just acquired normally and treated like just another Persona (even though he appears on the game DVD and in the credits). I admit that this is only arguably a flaw, but it just seems that these three Personas simply don't get the kind of special treatment they deserve. They seem to be the hero's equivalents to the Personas that everyone else in the game uses, so I wonder if it would have been better if they worked more like Junpei's Hermes or Aigis's Athena, which level up along with the Persona-user and transform with the plot, and less like normal Personas. If nothing else, it would have provided a reliable "always available" Persona (or three), which would at least be useful for showing off the hero's Persona abilities in plot scenes.
A much more pressing concern about the Persona system is that fusing Personas is just too time-consuming and annoying. My brother touched on this a while back, but one of the biggest flaws is the random nature of passing on skills through Fusion. Passing on good skills is essential, but it can take dozens of random combinations before a good combination of skills can be passed on (and even then passing on ideal skill sets is nearly impossible). In addition, it is impossible to even know what kinds of skills a fused Persona can acquire from its component Personas unless you go through this tedious process a few times. Trying to pass on a rare and powerful skill like Samsara or Thunder Reign through several generations of Personas can be difficult even without trying to pass on skills like Hama Boost or Elec Amp that are needed to get the most out of them. Trying to pass on great combinations involving three or more skills (like Auto-Maraku + Auto-Mataru + Auto-Masuku) is almost impossible. This issue just amplifies the annoying fact that it is hard to figure out what skills to give to a Persona that does not have a central theme to its innate skills. The whole thing would have been a lot better if the game was more explicit about the ability-transfer rules and it was possible to simply select the skills you want to pass on from a list.
One final point where the game has some room for improvement is the way experience is handed out to Personas. I think it would just be better if every Persona gained at least some experience from battle, rather than only the Persona you end battle with. There are ways around this limitation (such as the Growth skills), and the game does not really need it to function, so all it does is force the player to give the Growth skill to Personas he wants to build up a bit (a major annoyance given the system I just described above), or for him to use particular Personas in battle far more than necessary (and to the exclusion of many others). It simply intrudes upon the basic flexibility the hero has in being able to easily switch Personas in battle, and makes it harder to actually make full use of a full team of well-built Personas.
Anyways, I want to end this by saying that I really do like almost everything about the hero's Persona system. It adds an incredible amount of customizability and tactical variety to the game system, and can be a lot of fun. If it were just a bit more user-friendly, it would be an ideal game system for people like me who enjoy seeing the benefits of putting a lot of thought into building characters, and an equally ideal system for the plot and themes of the Persona series.