I've been playing my mage (my only main and max level character) since 04' so let me see if I can make some distinctions between the expansions of the Mage and it's subsequent specs during each time period.
Classic:
Fire - A Max range spec (40 yd) with side talents that benefited supremely from the increase of gear. Very crit dependent and wasn't the best raid spec until after Molten Core. Really shined in AQ 40m and especially Naxxrammas 40m with what we called "Rolling Ignites". Basically your ignite crit could be fed and stacked by other mages. So - whoever was the first one to crit on the boss, every subsequent crit by you and the other mages (we had 8 in Naxx 40m) would reset the timer and increase the amount of ignite damage the boss would burn for. On DPS race fights such as Maexxna or Patchwerk, we were stacking 7-12k ignite ticks which was an INCREDIBLE amount of damage for the time. Also shined in PvP for it's range, crit damage/ignite burns and of course the '3 Minute Mage' 1 shotters who used Arcane Power/Spell Damage+ trinkets/Presence of Mind and generally 1 shot whoever they sent their Pyroblast to.
Frost - I'm sure there were some Frost mage PvP'ers out there at the time..but it was really just a leveling spec for AoE grinding mobs. It had some good kiting techniques and it's last tier talent was Iceblock so it could help you in certain raid situations to break mechanics but after Molten Core, Frost really fell off as a viable raiding spec. Mainly known for it's Iceblock end-tier talent.
Arcane - Arcane was black in white so-to-speak. It was either 'Alright you're going full Arcane for Presence of Mind/Arcane Power' or You're Full Frost or Fire with the rest in Arcane to increase your mana pool, mana regen, and Evocation (which was something that had to be specc'ed in to!) Mainly known for it's Arcane Power/Presence of Mind/Evocation talents.
IMHO The heyday of what mages were - Glass Cannons. They could dish out the top DPS while not being able to survive more than a few swings from any 2her class and could get stun-locked 100%-0 from Rogues unless you were good of course
.
Burning Crusade
A lot of what Classic had carried over in to Burning Crusade with the exception of a few differences. For one, Elemental Mages sprouted up. These were Fire/Frost hybrids who brought a lot of different spells to the table rather than a deep singular tree with some side talents from other specs. It was by no means the best PvE spec but made for some generally fun/interesting PvP with being able to have some very useful spells from both specs (Impact,Blastwave,Ignite from Fire and Iceblock, Ice Barrier, Increased crit damage, and some effects/lowered CD times from Frost)
Frost shined in PvP with a some Arcane and a few Fire mages thrown in. And Fire shined in PvE with the exception of Arcane mages from Black Temple on to Sunwell (Espec. Kil'Jaedan).
New spells of note that were brought to the specs:
Fire - Blastwave, Blazing Speed, Dragon's Breath, Molten Armor
Frost - Water Elemental, Ice Lance
Arcane - Slow, Arcane Blast, Invisibility, Spell Steal
Mages were still topping charts for the most part in PvE, got even better in PvP with the exception of Warlocks (they were way OP) and got nice unique additions to their already fun specs.
Wrath of the Lich King
Wrath changed how the Mage specs were utilized and perceived. First, let's look at what new spells were brought to the table.
Fire- Living Bomb, Frostfire Bolt, Hot Streak(Vital talent)
Frost- Deep Freeze, Frostfire Bolt, Icy Veins
Arcane- Arcane Barrage, Mage Armor, Focus Magic, Mirror Image (Talents that made crit predicated on Spirit in addition to Intellect/+Crit items.)
Fire- became a much more AoE/Multiple Target-centric spec and was viable throughout all of WoTLK with it's crescendo during Heroic ICC/Ruby Sanctum where it was by far the best DPS out there.
Frost- was great in PvP as usual but was also a viable raid spec during WoTLK with Frostfire Bolt and it's debuff causing and subsequent Spell Power increasing talent Winter's Grasp.
Arcane- actually was the better PvE spec early on in Naxx 10/25 up until about Normal mode 10/25 ICC. It could be fed to incredible amounts by having 1 Arcane Mage being fed Innervates while the other mages (if there were any) being Fire. Spamming Arcane Blast was top shelf DPS with the Innervate strategy.
Mage was always a wanted class in raids, sustained top DPS throughout virtually every raid, and continued to be viable and at times overpowered PvP wise. Being fully Heroic ICC geared in BG's was like solo'ing Deadmines. The DPS with the increased AoE/Multi-Target Spec was so incredibly over-powered that to this day it still was some of the most fun I've ever had as a Mage.
Cataclysm
I was incredibly turned off by what Cataclysm did to the game, so I neither raided nor pvp'd at a high-end level during this time so my viewpoint may be a bit lacking and or skewed. As always take everything that is being said with a grain of salt.
Fire - Flame Orb
Frost- Ring of Frost, Frost Orb
Arcane-Time Warp, Ritual of Refreshment
Frost was glaringly over-powered throughout the whole expansion. With it's mobility, shatter combos, and numerous ways to bring stealthies out it was un-killable 1v1 and really shined in Arena/BGs.
Fire/Arcane/Frost were all very viable raid specs. Couldn't honestly say what was better during what time but they all seemed to have their place which made many mages happy across the board in that regard.
Mists of Pandaria
Mists of Pandaria. Not my favorite expansion by any stretch of the imagination, due to a few things. The removal of the older-style Talent Trees. It gave you less choice for what you wanted your character to be. Sure there was always "cookie-cutter" specs where theory-crafters had figured out what the best DPS spec was but you had options for flavor and uniqueness from other players of your class. That is still possible, albeit it's much more limited now-a-days.
The removal of Blast Wave. Blast wave was an incredibly awesome spell, not only for AoE'ing trash but also for PvP. It gave mages another avenue for kiting/pulling stealthed classes out and was an awesome mobility spell overall.
Taking Flame Orb away from Fire spec. See Blast wave reasons. ^^
Frost is as always over-powered in PvP and has really shined in AoE situations such as Challenge Modes.
Fire with high-end raid gear it's been fun to AoE farm, PvP in world situations due to the resilience change (lol), and just top meters in raids that Mages should be accustomed to by now.
Arcane I haven't played much of Arcane this expansion but from what I've seen it's quite over-powered in it's burst/sustained dps in Raids and it's Burst in PvP.
Overall Mages have been more fun to me than any other class hence why I've stuck with one main for the entire duration of this game. I sure wish some of the spells would be brought back and that Blizzard removes some of the bloat such as Alter Time, Ring of Frost, Time Warp. There was a time where every class was unique and brought something else to the table. Too much homogenization for my liking.