More than there used to be, that's for sure.
Some drinks list a “skinny” option. That usually means the flavoring syrups are reduced-sugar or sugar-free. Ask the barista if you're not sure.
Most of the sugar in Starbucks drinks comes from flavoring syrups of various kinds. You can always order the basic drinks with no sweetener — a plain latte instead of a vanilla latte, for example. Or, you can have it sweetened with an artificial sweetener like Splenda or Sweet 'n' Low.