Many puzzle games are set up like that. For example, the 7th Guest and 11th Hour. For the PSP there was Smart Bomb, which has a truly horrible user interface experience. There are also some sport games like that such as Konami's Track and Field series.

Warioware?

Marioparty?

Does Rhythm Heaven count? It's one game, with nothing but mini-games. There are many of this category.

Adventure-type game: Jewels Of the Oracle (only a little main story, get right to the puzzle hub)

Action-adventure type game: Zelda Twilight Princess (it has a LOT of main story, but also lots of minigames)

Online Social Gaming Site: NeoPets has the biggest minigame arcade of any virtual pet site or similar non-pet-themed sites like Gaia Online

Or you can go really oldskool - there were several atari, apple 2, and NES games where there were 3-5 games on the same cartridge, in some cases sharing much of their code. For example, there was a summer olympics game where the minigames were the different summer olympic events, ditto for winter olympics, there was the famous combat where the games all involved driving a vehicle to shoot at an opponent, and there have been several casino or arcade-favorite themed games. Most of those had minimal main story, but it's easy to imagine a version with more.

I personally have a lot of interest in using minigames for all the crafting activities of a larger game. A Tale In The Desert is a partial example of this - mining for example is a proper minigame, though many crafting activities are not.

Thank you for your help!

Warioware and Marioparty are more close to what I'm looking for.

But I want to find games where mini-games are more independent.

It is like in virtual casino, where you have slots, poker and black jack with common money and chips.

So I want game with a set of mini-games with common resources and maybe quests line.

Any ideas?