Spicy! I hear people talking about spice all the time and while there are spicy wine (ever have a cracked pepper filled Shiraz?) a lot of those sweet baking spice you find in wine come from... you got, toasty oak!
When a winemaker orders a wine barrel he can have it custom-toasted. There are significant differences between the flavors that a light toast or heavy toast barrel can impart to the wine it holds. Basically the heavier the toast, the more intensely spicy and smoky the flavors get.
Ginger and clove tend to be fairly common in wine and seem to be some of the most prominent aromas that you get from medium-plus toast barrels -- which, unsurprisingly, is probably the most common toast level.