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By "range of operation" of the transporter, I mean "distance up to which it could transport" or "distance from which it could transport something to its own location".
The range of operation would have increased with time without a doubt but I want to know the average range at any period. It'll be better if you provide full stats of all times.
From Memory Alpha's page on Transporters:
During the 22nd century, standard Earth transporter systems had a range of 10,000 kilometers; however, by the 24th century, standard transporter systems maximum range was about 40,000 kilometers, though a special type of transport, called subspace transport could beam over several light years. [...] Many 24th century starships were equipped with an emergency transporter system, but these only had a range of at best ten kilometers.
[...]
The maximum range of a transporter differs per species, depending on what kind of technologies they've used to build it. The transporter with the longest known range is that of the Sikarians, with a range of about 40,000 light years; however this was due to their planet's large quartz mantle which amplifies their transporter signal. Because of this, Sikarian transporter technology works only on their planet.
[...]
Gary Seven's mysterious sponsors on the Assigners' planet possessed transporter technology with a range of at least a thousand light years according to Spock. Scotty later noted that Seven's beam was so powerful it fused all of recording circuits, and therefore he could not say exactly how far it transported Seven, or even whether it transported him through time. Exactly how they achieved this effect remains unknown, since there has been no subsequent contact with them, and they hide their entire homeworld in some fashion.
[...]
The Vedala, one of the oldest space-faring races, also possessed transporter technology capable of beaming people and equipment to and from other planets (presumably in different star systems.) (TAS: "The Jihad") Dominion transporter technology, enhanced with a homing transponder, was said to have a range of at least three light years.
(Emphasis added)
Note; Gary Seven's people are identified as the 'Aegis' in several books & comics.
As Wikis mentioned, local factors can influence range, usually reducing it. (An exception being the Sikarians, who's planet's environment actually helps it.)
40 000 kilometres, according to The Original Series writers guide. Source: Wikipedia.
However, the range can be influenced by dense materials, solar flares, radiation, etc.
As a side note on transporter capabilities in the (in-universe) future, the Expanded Universe novels (particularly, the "Department of Temporal Investigations" (DTI) sub-series, written by Christopher L. Bennett) elaborate on transporter technology in the 31st century of (what is implied to be) the "real" future timeline of the Federation.
The short story "The Collectors" (in DTI, C. L. Bennett) makes it fairly clear that 31st century Federation can beam living beings at least dozens of light years (a transport from Earth to Tandar Prime, a long-standing Federation member world about 40 LY from Earth, is specifically mentioned).
Note that all tie-in material is considered a lower class of canon than the series and movies. Ultimately, whether or not one considers these works a "real" part of the main on-screen continuity is mostly up to the reader.
Also, the Federation of the 29th century, seen on VOY:Relativity (Season 5 episode, fully canon), possesses "temporal transporters", which apparently function much like normal transporters, with the added ability to displace the traveler in time. The temporal range is never specified, but the spatial range is at least sufficient to reach from the Timeship Relativity's position (location unknown; 29th c.) to Voyager's position in the Delta Quadrant at the time, [note 1] and effectively simultaneously to Voyager's position in orbit of Mars when it was being built.
Unless the Relativity moved in its own time to cover the spatial distance between transports, [2] the effective spatial range of its temporal transporters is at least half the distance between Voyager and Earth in late VOY Season 5, [3] and more likely, the entire distance or more; call it 40,000+ LY. It is also possible the temporal transporter's range is not limited in space, at least not when also moving the traveler through time (see below).
It is unknown whether the spatial range of the the 29th century transporter is dependent on the temporal displacement. [4] However, the temporal transporters are never seen to move people through space (like regular transporters) without also moving them in time in the episode.
Bear in mind that the foregoing is (insofar as that is possible, an attempt at) an internally-consistent in-universe explanation. Out-of-universe, I have to agree with the Comments to the OP, e.g. this from user Tyson of the Northwest:
The limits of Transporters are "what won't break the story", the capabilities of transporters are "what is necessary to move the story"
Unfortunately for those of us who like logical structure, consistency, and plausibility, ST is mass-market space opera, and the aforementioned virtues were about as important to the creators as you'd think that would imply (which is to say, not very). I, for one, periodically need to remind myself that if that's what I want out of a story, I need to go read some hard SF again for a change. :)
It is true that the writers' bibles (mostly-binding creative guidelines) for the shows included some fairly concrete limits on what transporters can and can't do, but even those specs primarily saw technology (including but not limited to transporters) from an artistic viewpoint, as a narrative device, not from a scientific one.
Notes:
Voyager Season 5 Episodes 16, in an attempt to beam out the away team they were within 600 KM and unable, they were ordered to move within transporter range. Now this was a Borg episode so I presume they needed to overcome structural limitations associated with the Borg facility, the only issue I see in this was their ability to beam in was not so limited.
