I love alchemy! At the beginning, when my character is vulnerable, I make resist fire, poison, etc. potions. Restore health & magicka potions are always useful, invisibility for sneaking around, poisons for tough enemies such as giants and briarhearts. Fortify smithing, enchanting, destruction, health, or magicka potions are useful. Fortify carry weight, for when you need to carry a little more. Regenerate health & magicka gives you an edge. I like to brew potions that combine effects, such as fortify destruction and fortify magicka. Regenerate health and magicka and restore magicka. Fortify sneak and resist frost (good for the draugr ruins). Fortify block and resist magic.
Besides being useful in themselves, alchemy is a major money maker, and a good way to level up. Most of the ingredients can be had for free. What's not to love?