If I thoroughly entertained you with my uber-geekiness
Yov, then it was well worth it!
And Aragorn's not your cup of tea, eh? Mine neither! I've never been drawn to him. He developed very late in the scheme of things, from a wooden-shoed hobbit, and was very constructedly propelled to be a successful King Arthur parallel. He's overshadowed by Gandalf for the most part, and when he is left to take over, his leadership becomes somewhat questionable. Nevertheless, is he "any more significant than a slew of other kings" as you say? I think he is, and more, so...
Lets begin analyses with Aragorn and the most dominant rulers of Gondor & Arnor in the 3rd Age... The list is extensive (Men of Gondor/Arnor being 17% of Arda’s total characters) so I’ll cut it short and include only the pinnacle, the top-50 Kings, Ruling Stewards, and Chieftains of the Northern Dúnedain. In many ways, Gondor is the center of Tolkien’s world, and its leaders are not unlike the Kings of England or even American Presidents. From a political standpoint, they represent the most powerful Men since the world was made round. Most attain their status due to military accomplishment or founding a land or a line; or contrastly, through military losses, or being last of a line.
Being strictly good or evil is not as prevalent here as in other spheres of Arda, but rather being pivotal politically. Then again Hyarmendacil I, who brought Gondor to the height of its power, is only 17th (167th overall); Atanatar II who ruled at the height of power and splendour is 19th (198th overall); and Tarondor who had the longest reign is 40th (328th). So there is definitely a mix of political opportunism, and strength of character. And this list includes many unsavoury and tragic leaders, again similar to English Kings & American Presidents: Aragorn is in fact nothing less here than a successful King Arthur!
His character is invariably good, but also politically very lucky! He literally transfers the World of the Elves benevolently to the World of Men. But more importantly he becomes, largely through actions in which he had a substantial hand, the 1st ruler of a Reunited Realm, severed for over 3000 years. He also has legitimate claim to the Kingship, re-instituted after nearly 1000 years. And by marrying Arwen, he leaves an heir whose relevance rivals (potentially surpassing) his own, and through both of them we envision the underpinnings of our own world...
Here they are, the first 7 need not be rehashed…
1. (5th)
Elessar Telcontar 1st King of the Reunited Realm
2. (30th)
Isildur 2nd King of Gondor
3. (40th)
Elendil 1st King of Arnor and Gondor
4. (48th)
Denethor II 26th Ruling Steward of Gondor
5. (93rd)
Romendacil II Minalcar 19th King of Gondor
6. (95th)
Meneldil 3rd King of Gondor
7. (96th)
Arvedui 15th and last King of Arthedain
8. (114th)
Anárion 2nd King of Gondor [Isildur’s brother; founder of southern-line & Anórien]
9. (116th)
Eärnur 33rd & last King of Gondor [defeated Angmar at Fornost; last of Anárion’s line]
10. (124th)
Eldacar 21st King of Gondor [half-Dúnadan, reign saw Kin-Strife; defeated Castamir]
11. (134th)
Eärnil II 32nd King of Gondor [defeated Haradrim/Wainriders; won Ondoher's crown]
12. (146th)
Rómendacil I Tarostar 8th King of Gondor [defeated Easterlings; slain later by them]
13. (149th)
Castamir the Usurper 22nd King of Gondor [captain during Kin-Strife; popular, but cruel]
14. (156th)
Mardil Voronwë 1st Ruling Steward of Gondor [faithful; instituted Steward’s Reckoning]
15. (157th)
Cirion 12th Ruling Steward of Gondor [granted Rohirrim Calenardhon for Oath of Eorl]
16. (161st)
Valacar 20th King of Gondor [sent North; married Vidumavi, precipitating Kin-strife]
17. (167th)
Hyarmendacil I Ciryaher 15th King of Gondor [last Ship-king; crushed Haradrim]
18. (190th)
Telumehtar Umbardacil 28th King of Gondor [inherited weaker realm; conquered Umbar]
19. (198th)
Atanatar II Alcarin the Glorious 16th King of Gondor [hedonist, neglected Mordor watch]
20. (203rd)
Falastur Tarannon 12th King of Gondor [1st Ship-king, strengthened Gondor’s coasts]
21. (206th)
Ondoher 31st King of Gondor [attacked by Wainriders & Haradrim; slain on Dagorlad]
22. (213th)
Valandil 3rd King of Arnor [perpetuates Isildur's line, but Meneldil maintains Gondor line]
23. (217th)
Denethor I 10th Ruling Steward of Gondor [saw Ithilien overrun by uruks]
24. (228th)
Arveleg I 8th King of Arthedain [drove back Angmar/Rhudaur forces, maintaining frontier]
25. (230th)
Araphor 9th King of Arthedain [with Círdan, drove forces of Angmar from Fornost]
26. (234th)
Aragorn I 5th Chieftain of Dúnedain [raised by Elrond, killed by wolves]
27. (236th)
Amlaith of Fornost 1st King of Arthedain [eldest of 3 sons who fought for Arnor kingship]
28. (237th)
Narmacil I 17th King of Gondor [son of Alcarin; all-powerful, hedonistic, lazy & childless]
29. (241st)
Aranarth 1st Chieftain of the Dúnedain [initiated heirs of Isildur to conceal their royalty]
30. (250th)
Argeleb I 7th King of Arthedain [reclaimed lordship over Arnor; died in battle]
31. (252nd)
Arathorn II 15th Chieftain of the Dúnedain [fathered Aragorn II; pierced by orc-arrow]
32. (258th)
Narmacil II 29th King of Gondor [brief reign, attacked by Easterlings; died in battle]
33. (263rd)
Boromir 11th Ruling Steward of Gondor [great captain, drove uruks out of Ithilien]
34. (275th)
Minardil 25th King of Gondor [slain in battle at Pelargir by Corsairs of Umbar]
35. (283rd)
Hyarmendacil II Vinyarion 24th King of Gondor [won great vistory over Haradrim]
36. (284th)
Araphant 14th King of Arthedain [renewed contact with Gondor, but little came of it]
37. (296th)
Túrin II 23rd Ruling Steward of Gondor [built Henneth Annûn, rebuilt Cair Andros]
38. (314th)
Hallas 13th Ruling Steward of Gondor [gave name to Rohan & the Rohirrim]
39. (326th)
Eärnil I 13th King of Gondor [2nd Ship-king; built great navy, took Umbar]
40. (328th)
Tarondor 27th King of Gondor [planted sapling of White Tree, longest reign]
41. (330th)
Argeleb II 10th King of Arthedain [let Marcho & Blanco settle in Shire]
42. (332nd)
Calimehtar 30th King of Gondor [won great victory over Wainriders]
43. (335th)
Ecthelion II 25th Ruling Steward of Gondor [allowed Aragorn to serve Gondor]
44. (341st)
Telemnar 26th King of Gondor [he & all his children died in Great Plague]
45. (354th)
Ostoher 7th King of Gondor [rebuilt Minas Anor as summer dwelling]
46. (356th)
Beren 19th Ruling Steward of Gondor [gave Saruman Isengard; fought Umbar attacks]
47. (364th)
Mallor 3rd King of Arthedain [during his reign Istari came to Middle-earth]
48. (375th)
Ciryandil 14th King of Gondor [3rd Ship-king; continued policy of ship-building]
49. (378th)
Araval 13th King of Arthedain [renewed Elf alliances; re-established Gondor contact]
50. (381st)
Arahael 2nd Chieftain of the Dúnedain [saw Dúnedain recovery, but Fornost's ruin]
I suppose the rulers of Númenor are next for analysis...