What are the benefits of alchemy?
Assuming that money is not a limiting factor, is there any use being an alchemist?
I ask this because in some other role-playing games, alchemy is just a waste of perks. What's the situation with Skyrim?
Depends on your play style, But I find there's a few potions that are well worth making.
- Healing Potions: In certain fights I find myself chain chug healing potions.
- Blacksmithing/Enchanting Temporary buffs
- Improved Carry Weight: For when you get to the end of a dungeon and need 10 more carry weight to fast travel back to a town!
As it happens, money isn't a limiting factor, Once you get a few points in alchemy you can level it very easily, and if you do it right you can actually make a profit doing so.
In addition to the other answers given, alchemy provides the single most game-breakingly overpowered exploit in Skyrim. It works because the effectiveness of any "Fortify X" enchantment on your gear is based on your restoration skill.
By enchanting a set of Fortify Alchemy gear you'll get stronger potions. If you use that gear to create a Fortify Restoration potion, drink it, and remove/re-equip your gear, the game will calculate a new higher bonus based on your improved restoration skill. You can then make another Fortify Restoration potion with the higher bonuses and rinse and repeat until your alchemy bonus reaches ridiculous heights. At this point you can create super powered potions of Fortify Smithing to improve your gear, Fortify Enchanting to enchant it, and any other overpowered potions you may desire. With this exploit you can level alchemy to 100 in under five minutes (assuming you have enough ingredients), and make potions worth 10,000+ gold each.
Warning: This exploit doesn't have an upper limit like stacking fortify enchant potions and fortify alchemy gear does. If you make your potions too strong the bonuses will grow larger than the variables the game uses to hold them. This does very bad things and will most likely force you to reload your game. I'd suggest not creating any potions with Fortify Restoration stronger than +100,000% or so.
UPDATE: The unofficial patch fixes this exploit.
I've only played as a mage-type character, and I have had no practical use for alchemy from the potions created. That said, I think that Alchemy is a great way to gain levels if you need to ("re-rolling" or gaining health / magicka / stamina quickly). For this, simply gather ingredients whenever you pass (I tend to press 'a' as I'm running by bushes, etc.) and stockpile them in a house. When needed, go make a ton of potions at once.
At the early stages, it's very easy to gain skill levels with the three 'manufacturing' skills. You can do the same with the other two: enchanting and smithing. At level 30, I have yet to use one of my own potions, enchanted items, or smithed items that I haven't found a better solution 'lying around'.
As @Neil says, though, it all depends on how you want to play.
Any character can benefit from healing/buffing potions and damaging poisons, but it takes considerable investment in perks (and time spent to raise skill levels) in order to make these powerful enough to make much difference, especially at higher levels. So I would recommend an "all or nothing" approach to Alchemy -- either count on spending 6+ perk points to make full-potential potions, or none at all.
However, even a novice alchemist with no perks selected in the Alchemy tree can benefit greatly from two effects -- Invisibility and Paralysis -- that can easily be produced with relatively common ingredients. It is much easier to gain access to these very powerful effects through Alchemy than through the Illusion and Alteration skills, respectively.