I work in Company A and I'm kind of the star there (I feel it is mainly due to political reasons). Recently, I received an offer from Company B and I decided to accept it. HR department in my current company pushed me to review my decision and propose conditions under which I would like to stay at company. 

I feel that offer from Company B is much better for my career (project is more interesting, company is also a better suit for me), but I don't want to burn bridges. How can I respond?
['https://workplace.stackexchange.com/questions/78863', 'https://workplace.stackexchange.com', 'https://workplace.stackexchange.com/users/-1/']
First of all, you don't have to tell Company A anything except the last date you'll be working for them.

However, you *could* say something to the effect of

> 
> I see this as a personal growth opportunity and a chance to experience different corporate cultures and different ways of doing things. I've thoroughly enjoyed my time at Company A (*don't say this if it isn't true!*), and may consider working here again some time.
> 
> 
> 

The idea is to spin this as "some years from now I'll be more valuable to you if I have this experience than if I stay here" - kind of like taking a really long sabbatical. Just don't be specific
The best thing here is to put it back on the company. 

> 
> I am not comfortable trying to define what sort of offer I would be
>  comfortable requesting. I would entertain an offer by the company if 
>  it feels that I am under-compensated currently, or should be advanced to 
>  higher position, and consider it appropriately.
> 
> 
> 

This gets the onus of action off of you, and places it it back on the company. If they make you an offer great, you can consider it. But as you said you are looking at more than just compensation. At the same time there might be a number possible that the company could offer you that might make you reconsider. Either way it should solve your problem of not wanting to burn bridges.