This "change" is called "re-sampling". This is pixel graphics, not vector; in particular, it means if you automatically re-sample 16x16 to any bigger size, the result will be prohibitively ugly in most of cases, almost always. Scaling down is more successful, but in such small sizes still questionable, usually needs manual re-touch. To me, all iconic images need qualification of a good artist and designer, and, for such small sizes, even all re-samplings. If some ugliness is your choice, you can do it in any graphics editor, but consider I warned you.
[EDIT: in response to follow-up question]
There are many products, free or open-source, to do that properly. For icons, I recommend IcoFx:
I tell you, the IcoFx quality is better then is simple approach, but manual re-touch is typically needed for really