Ashe should be able to take out just about any champion in the game, with little difficulty, so long as she is properly protected. It is important that every team have a carry champion, and Ashe is a great choice for that role.
Naturally, Ashe's mana pool is very small, and her regen is very low. Because of this, her abilities, that cost a pretty good amount of mana, are not normally spam-able (able to be used in quick succession). Greater Seals of Clarity are a great compensation for this, and allow you to avoid wasting gold on other mana regen sources.
Ashe is a ranged champion, and this allows her to stay alive if played appropriately. However, you do need to be able to attack, or you might as well not play. A great way to compensate for this lack of survivability is to increase her crowd control power, and increase her run speed.