I know of 2 locations:
There's the Butterfly Set in Majula, which requires you burn 2 bonfire ascetics to get the complete set
And then there's Gower's Ring of Protection, which is in the Shaded Woods after burning 1 ascetic.
That's all the locations I know. Is there a list somewhere of them all?
This should probably be community wiki.
There are multiple places you can burn ascetics, and depending on which items you are looking for is up to you. A list of places to burn and items you can gain are as follows:
Note: Since the release of SotFS I should point out that this only applies to the original version (some of the locations may have changed in SotFS) - and none of the DLC's.
Bonfire order (1st, 2nd, etc) is chosen from the warp locations.
Majula: Burning 2 Bonfire Ascetics will get you the Moonlight Butterfly Set and Moonlight Butterfly Shield. You must also speak to Maughlin and spend 16000 souls to get the Armour Set, while the shield will be in the Chest in the back of his house
Shaded Woods (2nd Bonfire): Burning 1 Bonfire Ascetic will get you Gower's Ring of Protection.
Shaded Woods (3rd Bonfire): Burning 1 Bonfire Ascetic will get you the Southern Ritual Band +2 when you defeat the area Boss.
Forest of the Fallen Giants (1st Bonfire)/Lost Bastille(1st Bonfire)/Shaded Woods (2nd bonfire): you can get the Heide Knight Set and the Heide Great Lance. These items need to be farmed, as any item can be dropped at a random rate. (Heide Great Lance can only be dropped by the Heide Knight in Shaded Woods).
Hunter's Copse (2nd Bonfire): burning 1 Bonfire Ascetic will get you the Clear Bluestone Ring +2 (need to defeat the boss again).
Earthen Peak (3rd Bonfire): Burning 1 Bonfire Ascetic will get you the Covetous Silver Serpent Ring +2 (need to beat the boss again). This bonfire is easily missed. It is above the boss fog gate behind an illusionary wall.
No-Man's Wharf (1st Bonfire): Burning 1 Bonfire Ascetic will enable you to farm the Shadow Set from the two enemies that spawn in the boss fight. You can farm this set by killing them and then using the Homeward Bone to warp out. You do not need to burn multiple Ascetics to farm this set
No-Man's Wharf (1st Bonfire): Burning multiple Ascetics will cause an invader encounter. This invader will drop the Visible Aurous Set. Multiple Bonfire Ascetics need to be burned to farm this set, and the boss must be defeated each time
Forest of the Fallen Giants (3rd Bonfire): Burning multiple Ascetics will cause an invader encounter. This invader will drop the Catarina Set. Multiple Bonfire Ascetics need to be burned to farm this set
Belfry Sol (1st Bonfire): Burning a Bonfire Ascetic will cause the Mad Warrior to spawn more frequently, allowing you to farm the Mad Warrior Set with more ease.
Drangleic Castle (1st Bonfire): Burning 1 Ascetic will cause an encounter in the Throne Room (behind Chancellor Wagner), with two Pursuers. When defeated, they will drop the Ring of Thorns +2.
Drangleic Castle (1st Bonfire): Burning multiple Ascetics will allow you to farm the Ruin Set. This set is not a guaranteed drop, but it is also possible to get this set without burning any Ascetics. If you do, the bosses (Throne W&D and Nashandra) must be defeated per Bonfire Ascetic. From bonfire intensity 2 and on, the Sentinels will only spawn once per bonfire ascetic, as opposed to 7 times on intensity 1.
Lost Bastille (2nd Bonfire): Burning 1 Ascetic after defeating the Gargoyles, they will drop the Covetous Golden Serpent Ring +2.
Sinners Rise (1st Bonfire)/Iron Keep (3rd Bonfire)/Black Gulch(2nd Bonfire)/Brightstone Tseldora(3rd Bonfire): Burning 1 bonfire Ascetic in each of these places will get you the Souls of the Ineffable when you defeat each area boss. These can be traded to Straid or Ornifex for spells or equipment. (Sinner - Old Witch's Soul; Iron King - Old King's Soul; Freja - Old Pale Drake Soul; Rotten - Old Dead One's Soul)
On a separate note: Chancellor Wagner will sell you the Wrath of the Gods miracle and Great Chaos Fireball pyromancy in ng++, but you cannot access these by burning ascetics. You can only get these by entering ng++ and speaking to him then after defeating the area boss.
There is also another amour set; the Dingy Set that is dropped by one of the two Black Phantoms that invade in ng+ only. This set will only drop once. Burning Bonfire Ascetics will not cause the invaders to spawn.
On which bonfires it makes sense to burn a bonfire ascetic highly depends on your playstyle. For example, some items only benefit mages.
There is a list of additional boss drops and other items on the wikidot page for bonfire ascetics. The additional drops are mostly rings and additional boss souls that you can trade for weapons and spells with Straid of Olaphis and Ornifex.
If you are a sorcerer, I recommend the Southern Ritual Band +2 at Shaded Ruins from beating the boss again and the Clear Bluestone Ring +2 from burning an ascetic at the Undead Lockaway bonfire in Huntsman's copse to fight the Skeleton lords again. You'll have more attunement slots and 55% faster spell casting.
