I have been positing a version of this
before, but now took the time to rework it a little with weapon ultimate suggestions for these new skill lines I thought up back in the day, and adding a few more skill lines I have been considering since...
Since this is another topic that keeps popping up and is dear to my ESO enjoyment ideals, I thought it might be a good idea to get my usual ramblings about these ideas into order and post a bit more fleshed out concept here for discussion and feedback... it is a very rough concept, I am sure there are many ideas in there that could use some refining and improvement, I just wanted to put it out there to show what I am talking about when I comment in those other threads...
Anyways, here are my ideas on the matter of what I would like to see added to ESO someday in terms of weapon skills, feel free to comment (please be nice!

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Polearms
These extra-long shafted weapons (…things like: Pikes, Poleaxes, Tridents, Glaives, Monks Spades, War Scythes, Ranseur, Military Forks, Naginata, Hunting Spears, Halberds, Spetums, Pitchforks, etc.) should have 50% more range then normal weapons, but be awkward to use in very close quarters, so any attacks that are made against opponents at knife range suffer a 50% damage penalty (meaning, the weapons will do half damage from zero to 50% normal weapon range, and then full damage from 50% to 150% normal weapon range… for light/heavy attacks, as well as skill use…)

Mounted Combat
This special "skill line" would be for using mounts not just for getting around and riding towards the fight, but also in combat... thus it is a bit different from other skill lines as it would not have a weapon of its own, but be mostly a collection of support skills and passives instead of weapon-specific active skills, with a main active skill that when toggled enabled mounted combat, meaning that characters with this skill active could draw weapons and use basic attacks, without becoming automatically dismounted. Normal skills would be unusable, though each weapon type (melee or ranged, mixed skills likes like One-Handed & Ranged or One-Handed & Magic can use both) would gain a special attack skill in the mounted combat line to use instead... but be otherwise limited to basic light and heavy attacks while mounted.
Note that ranged attacks while mounted suffer a chance to miss (I am thinking 25%, migrated 5% for each skill point, so the best trained horse archers/wizards would still have a 5% miss chance in the end - price of being mobile!), because it would be kinda harder to aim properly while on a galloping horse/bear/wolf/senche/whatever... which can be migrated through passives. But mounted combat -does- favor melee weapons where a mounts speed and power behind the blow makes a difference...

Brawling
Uses either fists, or weapons like brass knuckles, punch daggers, spiked knuckles, cesti, sap-hardened bandages dipped in broken glass, etc. depending on racial style; doing half of dagger damage with those weapons, or 20% with fists - this skill line is not supposed to be competitive with "proper weapons" on its own, but might make an interesting addition to ESO nonetheless, possibly even because of this handicap (not like there aren't enough class/guild skills to make up for it in any case). Quick jab light attack, long wind-up haymaker punch as heavy attack.

One Handed and Ranged
Uses a weapon in one hand and a throwing weapon in the other (offhand options for javelins, throwing knives, shuriken, throwing axes, throwing spikes, throwing irons, boomerangs, kunai, etc.), borrowing the first two skills from One-handed and Shield, then diverging in abilities; throwing attacks might be shorter ranged compared to bow or staff attacks, but could have an increased critical damage modifier...

One Handed and Magic
Uses your usual average melee weapon in the main hand, and a destruction wand or runestone (which could be two different options for two different effects, like... wands giving a bit of extra range, and runestones giving a bit of extra damage for example?) as offhand for a mix of magically charged melee strikes and elemental mid-range (meaning, half the range of a destruction staff attack) and AoE attacks or effects, all skills might cost half-half stamina & magicka unless otherwise noted, and heavy attacks restore half-half stamina and magicka

Twin Magic
If we have destruction wand/runestone as offhand for the above, there is no real reason mages could not take one of those in each hand, right? As alternative to destruction magic, mixing skills from those and the one-handed & magic skill line above, though with a reduced range compared to destruction to balance the gain of an offhand slot for traits and sets…

Martial Arts Magic
This is not really a weapon option known in the classic elder scrolls universe, it would be more fitting for a Japanese style anime, but... it might be interesting, they could very well add it with an "Akaviri" themed expansion, as it might fit in there... basically mixing brawling and magic for a truely "Melee Magic" skill line... the weapon for this skill line might be specially enchanted bracelets or mystic bands (which would need no crafting style as they would not appear by themselves, just as "mystic aura" around the users hands when "drawn" - and could be added to any crafting skill, like make jeweler more interesting...)
Due to its mix of physical and magical nature of attacks, this weapon skill line starts out as magica, but has many stamina morphs... it would be better as half-half, but... that is not really a thing in the ESO system...

Warding Staff
It seems somewhat clumsy to have a destruction staff as a main weapon as magica tank, so… why not give ice back to doing damage and slowing enemies, and make up a completely new weapon for tanky uses? One that uses magicka to block, obviously, and maybe has the taunt heavy attack, or maybe not (since it can get a skill for that).

In addition to those new skill lines, there are also a few more weapons that would fit right in with existing skill lines in some way... like...
Crossbows - could be added as alternate weapon to the Bow skill line as is (Maybe rename that one a bit… "Marksmanship", anyone?) Possibly with some tweaks… like perhaps increased armor penetration compared to bows, but a "reload time" after each shot? Possibly also changing the bows poison effects to disease for a bit difference in flavor…
Slings - another possible addition to the Bow skill line, firing heavy lead bullets, perhaps a bit shorter in range, but with some added effect to balance… again, the bows poison effects could be switched to a fire DoT, due to enchanted sling bullets (clay bullets that break open releasing volatile alchemical ingredients? Something like that…)
Short Spears - the Javelins from One-Handed and Ranged could also be useable as mainhand weapon for One-Handed and Shield to get a nice "Myrmidon" feeling - it would make a nice additional option for imperial characters, would it not? And while the animations may not be completely perfect... since we have "Puncture" type attacks with blunt-headed maces, I see no issue with having "Slash" type attacks with javelins, right?
Flails - could be an additional option for one-handed and two-handed weapons, though I am not so sure about how well they would animate I suppose... but if there were no technical difficulties, they could be done for an block-penetration effect, balanced by some drawback... possibly increased stamina costs (since it might take more strength to control such without hitting yourself) or maybe even a small chance to hit yourself on the backswing for each strike... this might include other "flexible" weapons such as Whips, Nunchakus, Urumi, etc.


Alternate Staves - we have fire, ice and shock as well as healing, but who here wouldn't want more? Cyan "coldfire" destruction staves (fire effect visuals in cyan, but less damage however done as oblivion type?), purple "warlock" destro staves (pure magic damage, with some "curse" debuffs and/or DoT?), green or brown (nix-hound spit!) acid destro staves (magica-based poison damage with DoT and some armor debuff?); sickly-bile-yellow "disease" restoration staves (do less healing but bonus damage as disease DoT), or red blood magic healing staves (less damage, but with a lifedrain effect)... possibly even give back ice to DPS and add a seperate "Earth" magic staff to cover the tanky effects? Or if we were to get the warding staves, those too could come in various flavors... indigo-turquise "alteration" as basic, maybe green-brown "earth-nature" with less defense but longer durations, and maybe a rainbow-ish multicolored "illusion" type that does add taunt to all attacks and some mental effects to its skills, but pays for it with less "warding" and effect durations?
Spell Foci - I always felt vexed my casters have to have staves to cast their castyness, I want another option! My idea would be a "Spell Focus" as alternate destruction/restoration (and warding) magic weapon, that used the exactly same skills (but possibly with different stats - like with wands / runestones, one weapon could have a bonus to range, the other to damage or spell critical or whatever... like, take a staff for extra distance to all spells, take a spell focus for extra punch...), but had different visuals... it would be held in the left hand, with the right making mystic gestures above it for casting, and depending on racial style it could be stuff like holy symbols, ornate spellbooks, meditation crystals, gemmed skulls, shaman rattles, ancient artifacts, gilded scepters, mystic constructs, daedric pact seals, etc. Naturally both in the classic flavors, and the alternate flavors I mentioned above... and these things would make -perfect- additions to the Jewelry crafting skill line...

Subduing Weapons - a derivation of bare-knuckled brawling, if they ever make a "unarmed" combat system for non-lethal barroom brawls (which are a classic cliché in every fantasy setting) there could also be less then lethal weapons for other skill lines. A small truncheon for one-handed, or a larger club for two-handed skills, a quarterstaff for polearms, or a stun-staff/wand for mages (sorry, no boxing glove arrows, for one that is DC copyright I would think, for another it is silly...).
These could also include “improvised” weapons of some sort... a frying pan, a broomstick, a coin purse, a candlestick, a chair leg, a belaying pin... might be interesting for some special "no weapon" areas quest thing - go in unarmed, find your improvised weapons there...