GTA2 - top down game that is just like GTA
There aren't many to be honest.
Super Runabout is probably the closest GTA type game in that you have A series of missions in San Francisco and a variety of cars to choose from. However you can't get out of the vehicles etc and the missions are more clearly defined but it is an open world to drive about in. I.e. You can choose your own route and go wherever you want.
Urban Chaos is a terrible port of the PC game which is a shame as it could have been half decent. You get vehicles and on foot missions. Shame as it could have filled a decent niche but it is a constant battle against the controls and the game logic etc
HeadHunter is a really good game and is like a mix of Metal Gear Solid and a semi open world that you drive around on your motorbike, I suspect the biking section was going to be more substantial than it ended up being, indeed during previews they talked about online races etc, but due to the hardware cancellation I think they just finished what they had and got it out there. Great game though.
Omikron: The Nomad Soul is an interesting game in that there is quite a lot of flexibility in the game. Use an item you needed for a mission and you can buy it again in the shops, several ways to approach missions and a blend of one on one fights, third person adventuring and more. Again it is a Quantic Dream game so never quite delivers. Has some really interesting ideas and is fun to contrast with the two ShenMue games to see the different approach of Japanese and Western developers.
In terms of games like Zelda - probably ShadowMan (which lots of people love but just never grabbed me) or Soul Reaver.
None of the above really fit your original post but might be worth checking a few of them on YouTube and seeing what you think. Will have a think if there is anything else out there.