A lot of studios are a Work-For-Hire business model, where they don't really get to decide at all what they're going to make. Instead, you find publishers/IP-owners who need studio to make a game for them, and then you create a pitch to try and secure that work (which may involve making a GDD/TDD, concept art, a budget, and even a small prototype)... and then hopefully your studio is selected to make the game.

At self-funded studios, it will usually be an executive/director who makes the choice of what game to make next -- CEO (managing director in real English) or creative director, etc... Hopefully though, the design and concepting teams would have a lot of input in the process, and even flesh out a few different game designs before one is chosen.

Might I add that successful vendors still have a strong say regarding which opportunities they will pursue?
I've been places where they had to pitch evertime and others where they passed on a lot of things.
In both cases, the call came from the CEO or president who represented the AC's interests.

While designers and executives tend to get the big picture details, those who implement the details are also critical.

Programmers will always have a say in the details of the design because they're the ones implementing those details. If the programmer implements it differently than designed, then it is implemented as the programmer implemented it. Those minor details have a big impact on how a game feels.

Animators and artists also have a big say. While the art director, lead designer, and other leaders can issue guidance and set big standards, the individuals on the team have their own nuance.

Even as individual animators I worked side by side with two: one animator was also a dancer, participated in ballroom dance teams in college and continues in ballroom events to this day. Before animating anything he would record several video angles of himself doing exaggerated motions and exaggerated postures and facial expressions. Then he would review those as he worked to make animations that were over the top fun. Another animator worked next to him on my team. He would usually pull a clip from youtube or similar to seek real-world accuracy. His animations were never as dynamic or expressive, but accurate to real life. Both animation styles fit the art direction et the differences were noted by our customers. The first one's work was frequently called out in the forums with comments like "I love when my sim is cooking on the teppanyaki grill his animations are so funny", versus "those actions are so realistic".

Minor implementation differences can have enormous impact on the final game, and it is the grunt workers who implement all those details.

I don't think anyone has really covered how it works in a small indie studio yet.

The smaller the studio the more creative control you're going to have, i've always worked alone, or in a very small team and all the game ideas start out in my own head. If you want this level of creative control you're going to have to sacrifice the idea of working in a large team, as with all real world work, working as a team requires compromise.

Hope this helps!

In my team, the game designer tells us what areas need work. He is not a micromanager but expects us to complete areas or lists of things. Sometimes he has something specific to do. He does offer his views on a regular basis about the quality of the product or techniques to use. The developer works almost exclusively with the designer. We rarely get anything directly from him and vice a versa. Our team members are mostly hundreds or thousands of miles apart and work thru the Internet, including conferences online. A couple guys live only about 1 hour from one another in Germany and sometimes meet in person, but that is the exception.