There is no comprehensive list. Please add on ones missed, while quoting previously mentioned ones.
Riders of Rohan-Do not coint towards limit
Azog's Hunters warband-Half may be armed with bows, but 1/3 of your total force can be armed with bows.

However, I know I missed some. Also, is there one for the Rangers of Gondor, like the Riders of Rohan? They both come automatically with bows...

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By all that you hold dear on this good Earth,
I bid you stand, men of the West!

No, there is not an official comprehensive list of exceptions to the 1/3 bow limitation. If an exception exists it has to be found in either the source books or FAQs. They can be model specific, any army special rule with model limitations, or a army bonus. There is no exception of Rangers of Gondor or just any model that comes with a bow in its starting kit. Some of the exceptions do seem to be intended to address the sort of models that come in each box. Easterlings and Harad have more bowmen per box than they would be able to use otherwise.

Rohan - Riders of Rohan do not count toward.
Arnor - Player may choose to bring up to 4 rangers of Arnor for every Dunedain or Ranger of the North in the same army.
Harad - Player may choose to bring a certain selection of harad units and bring up to half with bows.
Easterlings - May field 50% of their army with bows.
Mirkwood - Ranger captains, Tauriel, and Legolas can lead rangers of Mirkwood without those rangers counting toward the bow limit.
Household of Elrond - Rivendell Knights do not count toward the bow limit.
Azog's Hunters - If a players army consists only of models for the Azog's Hunters list then he/she may field up to 50% with bows rather than 33%.

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"Draw your sword with a heavy heart, but swing it with a heavy hand"

Are you sure? I'm fairly certain that Easterlings don't get any special rule for their bow limit. I think Khand did in the special (and one-off) army rules for Throne of Skulls last year. Is that what you mean?

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"There are few left in Middle Earth like Aragorn, son of Arathorn." - Gandalf, Many Meetings

"Eastern Kingdoms Warband Rules
Easterling Warriors, in warbands from the Eastern Kingdoms
army list, have a Bow Limit of 1/2 rather than 1/3." (FAQ for the Fallen Realms, pg. 1.)

It seems I did miss remember the rule. It is just Easterling warriors and I thought it included the Kandish as well. It is just a rule for the Eastering warriors themselves, however, not a army rule.

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"Draw your sword with a heavy heart, but swing it with a heavy hand"

Many thanks. But seems odd rangers og Gondor/Ithilien do not get a special rule... They all come with bows like the riders of Rohan.

_________________
By all that you hold dear on this good Earth,
I bid you stand, men of the West!

Huh. I was completely unaware of that. Makes me wonder what other rules I've missed in FAQs.

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"There are few left in Middle Earth like Aragorn, son of Arathorn." - Gandalf, Many Meetings

I want one for any Ranger figures... Ithilien most of all. I mean, you see them and only rangers of Ithilien attacking Haradrim.

_________________
By all that you hold dear on this good Earth,
I bid you stand, men of the West!