Which Pokémon really needs that special, in-battle boost that Mega Evolution can provide? Which stats would increase, and would it change its typing? What would it look like? Let's get weird with it.
The legendary birds. They would probably stay as the same types, but I see the possibility of them changing into dragon types. This is what I think of the stats: Articuno: HP: 90 (+0) Atk: 85 (+0) Def: 120 (+20) SpA: 125 (+30) SpDef: 145 (+20) Spd: 115 (+30) Total: 680 (+100) I decided to boost Articuno's special attack and speed, mainly because it's typing is more offensive than defensive. Attack is pretty useless, as 90% of its movepool are special attacks. Didn't boost HP either, as most mega mons don't have increased HP. Zapdos: HP: 90 (+0) Atk: 120 (+30) Def: 95 (+10) SpA: 145 (+20) SpDef: 100 (+10) Spd: 130 (+30) Total: 680 (+100) Zapdos really needs an increased physical attack, as it cannot learn flying type special attacks via level up (and still very few via anything else). There should also be an increase of speed, as 100 is still pretty mediocre compared to other stronger mons. Defense doesn't need much boosting, as it can pretty much outspeed and one-hit-KO any weaker Pokémon. Moltres: HP: 90 (+0) Atk: 120 (+25) Def: 100 (+10) SpA: 145 (+20) SpDef: 100 (+15) Spd: 120 (+30) Total: 680 (+100) Moltres' stats are pretty good in general for its movepool and typing, so it doesn't really need any emphasis on one particular stat. I chose to give it's speed stat the most of the 100 points, since it's the only thing that it's lacking to become a good sweeper. Please excuse any Mathematical errors, I did not double check this.
Well aside from all starters which I know a lot wants megas for, maybe give one to some of the pokémon that could really use a power boost. Like Dunsparce and Luvdisc, especially Luvdisc I doubt it would ever get really viable in anythign but maybe it would make it useful in-game at least.
Raichu I feel is underwhelming in battle and entirely unloved because of Pikachu's popularity. Giving it a sharp boost in speed and offense and perhaps a unique ability could really give it a day in the sun. Rapidash isn't the most popular, but I like it. That's most of my argument. As a concept though, how about making it into a unicorn-pegasus? Fire-Flying and with astronomical speed, plus maybe Drought as an ability to give it some Apollo's Chariot theme. Eevee could get a mega form even though it's not fully evolved. Eevium Z tried to give it some battle utility, but Mega Eevee could be the Normal Eeveelution we've been waiting for. Jynx was, in Generation 2, seemingly part of a trio with Electabuzz and Magmar, all of them having similar stats, being humanoid, and getting baby evos. Then Gen 4 came and left Jynx behind with no evo like the other two got, likely for being the odd woman out with two types and somewhat different stats. A Mega Evolution could put them somewhat on par again, similarly to Dusclops (who got a full evolution in 4) and Banette (who got a mega evo in 6). Also, that unique typing is not easily replaced. Flygon would be great with a mega form. I can't decide if Mega should push it more into a Special Attacker or Physical Attacker direction (I slightly prefer Special in this case), but it certainly deserves some love, especially after living in Garchomp's shadow so long. Cacturne has potential to be changed up completely, and here's how I would do it: shed the Dark typing entirely in favor of Ground or another Sandstorm-surviving type, replace its abilities with Rough Skin, and make it very defensive to use with Ingrain. It could have some serious staying power on the field. Hippowdon also has some sandy theme, but I don't know how to improve it. Just don't let my favorite hippo get forgotten! Dragalge, although introduced in a generation that only got one mega evolution (since they were focusing on 1-4), could benefit from a mega evolution. I get the feeling that Gamefreak figured that its awesome unique typing got shafted by unfortunate stat placement, and that's the entire reason Naganadel exists. Would be nice to give the original its due.
Nidoking and Nidoqueen are definitely candidates. Also Arcanine since it's classified as The Legendary Pokémon for its species. I'd also enjoy seeing some more of the Gen 4 evo Pokémon get Megas, especially Electivire, Dusknoir, and Yanmega since those three are the ones that I feel have the most potential for Mega Evolutions. As for typing and stats, I don't know much about stats, so I'll just stick to typing. Nidoking and Nidoqueen would be good as Poison/Steel types, with Steel being added as sort of a royal thing (They do have king and queen in their names), or they could just as easily stay Poison/Ground just with new abilities. I can see Mega Nidoqueen having Queenly Majesty for her ability. Then for Arcanine, I feel like it would likely stay a pure Fire type. Not sure about its ability, though. Maybe Drought? Idk. Electivire would probably stay an Electric type, or otherwise become an Electric/Fighting type. That could be cool. Then Dusknoir would definitely become a Ghost/Dark type with probably a Grim Reaper style of appearance, and Yanmega would be a Bug/Dragon type because, well come on, he's a dragonfly! Man, I really wanna see a Mega Yanmega now!
Because they were Generation VI's "gimmick", I doubt we will ever get more Mega Stones. But if we did, then I would suggest, first, all starter Pokémon. Only the Gen I and III starters are currently covered. That leaves five current generations of starters uncovered by Mega Evolution. Other than that... there's a fair few I feel could use a power up. Flygon definitely is missing, but I think Sawsbuck would be an interesting choice. With all four of its formes, and a new ability that makes it require less set-up, there is a lot of interesting potential.
Mightyena, then maybe it would end up a decent mon, plus I really like Mightyena. This goes for a lot of early route mons really, plenty could benefit from getting a mega.
I really wish Sylveon would get a mega evolution. If it does, its size will increase a bit as well as its ribbons will get longer. The power of its fairy wind will increase that it can even blow a huge wall.
Maybe Base form of Kyurem can get a mega and evolve into the original dragon from the legends. Cool thought.
Dunsparce should get a Mega that catapults all its stats into Ultra Necrozma levels. Because that would be absolutely amazing. Poor Dunsparce.
Sawsbuck, because this Season concept has so much potential for a mega (I made a custom mega for it that shows that even with some small ideas, you can make an awesome mega from it).
We need a MegaStick for MegaFarfetch'd. I want Pokémon that really need them to shine for their first time, but also for those who sadly lost their spot long ago. Things like Vileplume or Beheeyem are good examples for the former, while Tauros or Electivire are for the later. Also worth mentioning: thingies like Qwilfish deserve much more than having a mega to, later, let them alone in the corner all over again like they already did to others. (I know, Qwilfish has been surprisingly good lately, but one thing doesn't exclude the other.)