There are two main styles, Fino and Oloroso. Within these two general categories are several subcategories. Lighter styles are typically fortified to around 15% alcohol while the richer styles are often fortified to around 20%.

Fino

Fino sherry is dry, light, crisp, and tangy and makes a wonderful aperitif. Flavors are typically mild yet distinctive and can include dried fruit, apples, and nuts.

Manzanilla is typically even drier, offering a bracing, salty tanginess due to being produced in the coastal town of Sanlucar. Flavors are similar to regular Fino.

Amontillado usually refers to an aged Fino and will be darker and richer with nutty toffee flavors and sometimes a hint of sweetness. 

Palo Cortado is still dry but richer than Amontillado with notes of raisins, coffee, and mocha.

Oloroso

Oloroso sherry is darker and richer than Fino although most examples are still dry. Flavors include raisins, dried figs, prunes, coffee, dark chocolate, and toasted nuts.

Oloroso Dulce and Cream sherry are both moderately sweet dessert wines whose flavors follow closely to dry Oloroso with the addition of caramel and toffee notes.

Pedro Ximenez  

Pedro Ximenez is often almost black in color, concentrated, and intensely sweet. Flavors include simple grapey sweetness, raisins, coffee, dark chocolate, caramel, molasses, and soy.