Even though most of its iterations have only a few characters, the Final Fantasy series yields some interesting trends after some analysis. Recent FF games have often given the player a group of six or seven highly customizable characters, yet only let the player use three of them at any given time. Many players have realized that there is no drawback to focusing on building up and using only three of the characters (half the team) and ignoring the rest; in fact, it is an advantageous strategy. In an environment like this, giving the player an optional character late in the game is not a very meaningful reward.
And yet, there is one Final Fantasy game that did reward the player with optional characters: Final Fantasy VI, which had fourteen characters in total, far more than any other Final Fantasy. Arguably, all but 3 of these characters are optional, since the player has to undertake many optional quests to recruit/regain most of them in the second half of the game. However, the game gives the player strong incentives to use all of these characters, and rewards the player for seeking out the most elusive and optional ones.
First off, all of the characters in FFVI are very different mechanically. Not only do the different characters have wildly varying stats and equipment, they all possess powerful, unique special abilities. Some of them, such as Gau, even operate under very different rules than other characters. So, choices about which character to use can go beyond mere personal preference.
Second, FFVI gives the player situations where using different party combinations is advantageous. The Tower of Magus, for example, is a dungeon where only magic can be used. So, a party of nothing but strong magic-users is a good choice to use for clearing it. A party of nothing but physical fighters would work poorly.
Third, there are points in the game where the player can actually use more than a few characters at once, or on alternate paths. In a military battle a quarter of the way through the game, in the Pheonix Cave, and in the final dungeon, the player can switch between up to three teams. Thus, the player can actually make use of having a lot of characters.
Finally, the game forces the player to use certain characters in his party at various points in the game. The player has to send Locke and Celes to the Empire or use Shadow on the floating continent for example. While it takes control out of the player's hands, it both forces the player to keep certain characters in use, and gives the designer a chance to make characters more developed by including them in the story.
Many successful games built around having many characters employ these at least some of these four techniques. Here are some individual examples:
Super Robot Wars Original Generation 2 does a good job of mechanically differentiating its various characters and mechs. Some mechs can dodge almost anything, others can absorb huge amounts of damage, while others can attack numerous foes at once. While mechs tend to fall into general categories, they all have individual quirks and uses.
Chrono Cross is actually very good at encouraging different team choices. Since most dungeons and bosses are dominated by a single element, it is advantageous to always bring at least one character with the opposing element (to attack with) and one character who is of the same element (who resists attacks).
Suikoden III is a great example of a game which gives the player opportunities to use lots of characters. Not only does the mass combat system let the player field up to ten units of five characters each, the multiple perspective system of the game lets the player use various different teams. Not to mention the final dungeon forces the player to create three teams which each challenge their own major boss.
Again, Super Robot Wars Original Generation 2 is good at using the story to make the player use certain characters. In almost every stage, the game forces the player to deploy one or two specific characters who have their plot developed a little more along the course of the battle. So, the player is encouraged to use almost every character.