Accepting and refusing politely may depend on what you are asked.

For example:

Would you like some cake?

Yes, please.	No, thank you
Sure. Thanks	I’d better not. Thanks anyway.
Okay. Thank you	No, but thanks for offering

Would you like to go see a movie?

Okay. Sounds good.	No, I’d rather not.
Sure, I’d love to.	I’m sorry, but I can’t.
Yeah. Good idea	No, but thanks for inviting me.

How about some more pie?

All right. Thanks	No, thanks
Looks good. Thanks	I’m really full, Thanks anyway.
Don’t mind if I do.	Looks delicious, but I’ll have to pass.

How about going skiing this weekend?

Great. What time?	Sorry. I’m busy this weekend.
Sounds like fun.	I don’t think I can.
All right. When and where?	How about some other time?

See also :

Speaking : Inviting, Offering

Textbook Recommendation : Touchy Situations, Chapter 7