When you think of "games," you tend to think of winning. In most games, that's the only goal. Like Chess. There's no allowance for wanting to make a pretty pattern with your chessmen... or bonus points for resurrecting captured pieces by fully advancing some pawns. If you're not playing towards the goal of winning - capturing the enemy king - you're going to lose and thus the game will end. Or Football. The sole point is to move up the field and score touchdowns. (Although I suppose it could be argued that individual players are working towards the separate but compatible goals of improving their statistics.)
The next step up would be games with a primary goal and several secondary goals, that may be completed either before or after the primary goal. Like the Crash Bandicoot series... the primary goal is to beat the game by progressing through every single linear world, but you can also try for 100% box destruction or crystal collecting. You don't have to smash all the boxes to achieve the primary goal, but it's there for an additional challenge.
Beyond that are the games where the lines between primary and secondary goals are so blurred that they create the illusion of *no* goals. Or at the least, there is so many fully-developed secondary goals that to persue any of them is to create your own custom primary goal. Here's three games that I think fall into this category or freeform gaming.
The Sims made a huge splash some years ago on the platform of goal-free gaming. On the surface, you're able to lead your Sims in whatever direction you wish. In hindsight, I think that promise turned out a little hollow. The only real meaningful activity is expanding your house and keeping the people happy. The only way to accomplish this is to get a job and make money. If you don't get a job, if you don't buy furniture and talk to neighbors, you end up not doing anything. The game actively discourages non-working by throwing lazy people into fits of boredom, insanity and eventually death.
The true venue of freeform here is your ability to customize your gaming experience, both inside and outside the game itself. You can choose from a wide variety of furniture and personality types. You can make your own skins, music, pictures and incorporate all of that into the game. Tons of websites out there are constantly offering up new items to download. I would say that the presentation is the real freeform playhouse here, not the gameplay itself. The daily grind of The Sims eventually degrades into a high-pressure repetition of friendship management. Yes, the near-endless series of expansions has helped add new gameplay elements, but as I've said before, having The Sims plus all of the add-ons is one hell of an expensive game.
Grand Theft Auto 3 has a strong primary goal: work your way through the storyline missions. But instead of connecting every mission end-to-end, you're allowed to effectively put the plot on pause and wander about.
The secondary goals all exist in this "wandering" state. The entirety of the weapons and vehicles are at your disposal, and the city is programmed to continuously react to your actions. In reality, the engine that runs the missions is still working when you're between adventures, which means the "inbetween" portions can be just as deadly and challenging as the primary missions.
That inbetween part is the freeform state. You can tool around in Liberty City infinitely, and the game provides several secondary goals to work at completing. The 100 hidden packages, ferrying taxi passengers, street rallies, etc. But you are more than welcome to just tour the city, drive around like a maniac, and shoot and kill at whim. Unlike The Sims, it truly is the gameplay that's fluid here.
The MMORPGs/RPGs fall into this particular sub-division. Generally there is some kind of plot to slog through, or at its base, the simple advancement of your character's skills. But beyond that is the various mini-games, item collecting, tournament combat, career/alignment tracks, and relationship building.
But right now, Animal Crossing is the high water mark of freeform gaming. Unfortunately, the concept here (living in a rural village of anthropomorphic animals) may cause some gamers to think it's not a compelling title. There is no overarching storyline; there is no end. There is no villain; there is no conflict. You are free to create your own path based on the game's provided boundaries.
If you're going to define secondary goals as goals that you never actually *have* to complete, then Animal Crossing is almost entirely secondary goals. You can keep opening mortgages with Tom Nook so he'll keep making your house bigger. You can catch fossils and insects to complete the town's museum exhibits. You can collect sets of coordinated furniture so you get a high rating from the Happy Room Academy judges.
But the game isn't going to end if you complete any of these tasks, or even if you complete all of them. It's never going to end. So what's the point, right? The point is to live... which is a decidedly different approach to gaming. Once you start to realize what the game is capable of, you instinctively start to apply your own goals. For example, I'm trying to get all my villagers to wear the same clothes. Rhonda spends hours fishing, both to sell and to hunt the rare ones. Even just wanting to see AC reveal itself across a year of real time is a goal in itself.
There is no perfectly freeform game... they're all naturally limited by the game's own scope. But I really like the liberation of games without an end, yet with enough variance that it isn't just the same game every time, like Diablo 2 or Unreal Tournament. The newest patch for Warcraft 3 adds a difficulty control for CPU players. To my freeform thinking, this means you can now slow down the expected CPU downpour and actually start experimenting with the game itself. (Which before you could only do if you were in a multiplayer game with like-minded, non-aggressive players.) Like building an army of just Orc Wolf-Riders, or without any heroes. Or actually getting all those high-level spells. How about trying to hold the town's defense with just peons? These are the sorts of tactics that would get you laughed out of the battle.net chatroom under normal circumstances. But with a less restrictive environment, you can have the freedom to develop new ideas - fun ideas - and stretch the game's potential.