How do you save your final logo in Adobe Illustrator as a vector?

You see i have traced an image in Adobe Illustrator, now i want to save that logo as an image thus allowing me to expand it and decrease the size without losing quality as a vector. I use to know how but my days at school have long gone.How do you save your final logo in Adobe Illustrator as a vector?
just hit save. it must be an illustrator or eps file. If you export it as a jpg or any other ';image'; file, it will lose the ability to be resized without losing quality.