Lux, Swain, Morg, Aniva, Gragas, Elise, Oria, Karthus, Xerath, Kat, Ryze, Brand, Zigs, Zyra are the mids i play off the top of the dome....

Zyra is amazing. She can get countered, but she also counters many people. She has one of longest ranges in the game with her q/e combo at full range, you can poke successfully from a distance further than viktor's lazer or xerath. She has a snare, and her plants can easily shut down a jungle path, aiding in team escapes or team engages. Her ultimate is a massive AOE pop-up that when used with her plants can certainly burst down almost anyone on their team with the exception of maybe a very tanky top champ/jungler. Her seeds grant vision to scary bushes so you don't have to face-check them. She can farm safely with her plants while being well out of the range of most mid champ's spells. If you get into a duel that you know you will die from you can lay down as many seeds and spells as possible and usually pick up the kill with your passive which does massive damage late game. Zyra is a bucket full of win. Try her in 3's because her plants/ult on top of one of the alters will certainly guarantee that the other team can't capture it back or take over yours.

Viktor is a very strong mid champ too, but he takes a bit more skill to play I think and his cooldowns are pretty bad. But I have certainly done the most damage with viktor than any other champing. You can half health the entire team with your lazer and then half health them again with his ult. Not to mention his gravity field has an insane amount of utility. Viktor is super underplayed and underrated.

I would say go for:
Galio and/or ryze for tanky AP if your team is lacking tanky-ness
Akali, Diana, Talon, Kassadin, and/or Katarina for midlane assassins.
Morde, Anivia, Galio for pushing lanes (if their mid has weak minion killing skills like leblanc).
Ahri, Annie, Galio, Anivia for strong CCs

There will be people that won't agree with me, but it is my opinion.
I'll say go with a character that has hard CC, since sometimes junglers won't have that good of a CCs with them for a good gank...

have fun :3

Or you can play akali and counter them all. Defensive play till lvl 6 just throwing your Q, they get all confident that it will be a passive lane then once you hit 6 and have 3 stacks, BAM.

There have already been many good choices mentioned, but one i would add would be kennen. He can outlane practically every other ap mid in the game (except for Mordekieiser of course). His thunder shuryken is great for harassing and getting last hits.

The downside is that Kennen is fairly squishy and has a steeper learning curve than most other ap mids, since he is energy based. However, once you learn him, he is great.

Syndra...is a Monster. I seriously don't get why she's so undervalued. I can't even find a downside to her. It's like a long ranged annie, with a skill shot-skill shot stun. Hard to hit stun, but still.

Fizz, Gragas, Morgana, Viktor, Zyra, Kassadin, Annie, Diana. Also, go top with Swain if they pick Fizz.

Ahri, Ryze, Morgana and Gragas are safe picks.

Something that is really strong is a good Cassiopeia. Her harass is strong, her potential to take out squishies like AD/AP champs is amazing, and built right, she can even lay some heavy damage on Bruisers. You can build Rylais, Unholy Grail, Rabadon's Zhonya's and another item to give her some decent defenses while granting her utility with that slow.

Another good one is Anivia. The AoE ult, when placed properly in a team fight can really force foes to reposition or take decent damage (Though after a few seconds it really hurts) Her wall can completely change team fights, and she has strong early/mid game burst. If well fed, she continues to keep the damage up until late game.

Akali is one you might want to learn, as well as characters like Galio and Talon in the case that you have someone like Rumble or Vlad top. He can really shut down Mid champs, and I used to build him kind of Bruiserish to the latter part of the game.

I don't think I saw Veigar or LB. Those two are the AP burst mages-LB is early game domoniation, and late game assasin. Veigar is ok early, to farm up his AP, and late game he just booms.

Ahri, Kat, Akali, Diana, Karthus, Gragas, Kassadin, Mord, Zig, Fizz, Ori, Morg, Ryze, Zyra, Swain, Annie, Syndra, Malz, Anivia (God that passive GA), Thresh, Eve, Cass, Vlad (But top is better, because most solo tops are tanky melee, but his tanky AP with super sustain, though damage is not as amazing as others), Zed, Brand.
All i can think of right now for mid champs you should try. I don't own all of them, but 95% of them, though I obviously faced them all and used them for free before.
Fav:
Akalia- Energy base, u can trig both her innate with mastery and runes, free spell vamp lvl1, has stealth and can be super hard to kill at lvl4 while she pwns lane most of time at lvl6. Has triple blink.
Diana- Tanky for a AP mid. No cd ulty for blink and has a refresh shield to win unexpected fights. A gap closing slow makes it impossible to escape alone, unless for flash or summoner spells. Q is odd but the damage is decent.
Brand- Just beast passive, high damage out put and strong CC (takes skills to make the aim, but really scary when pull off). Farm power is great and easy to harass. 3 AoE skills, while ulty is just ridiculously. The downside is the squishiness but he has nice cast range. His also really mana hungry.
Cass- Only downside is the need of mana. 2 spammable skill during lanning, while increase movement will allow her to easily trigger her E. W is quite useless until u have ult, but it can zone and lock down path ways, help team fight, or escape. Ulty is not the best in the game, but pulling of the immobile is deadly as hell. While escape, if have rylais, u can keep spamming Q till u think u can win a fight, just E a lot of times
Eve: Last but no least, I don't play Eve that much as a Mid, though I do sometimes. Stealth is key and piss many ppl off. She does fall off late game, you are warned.Though her early power in limiting the enemy mid is strong, unless u fight someone like Zyra or Heimer who spammes unit or a mage counter pick like LB or Kass. Her Q is piss off for farm, chase damage. E is just strong, W solves the limited stealth and chase. Mana is np because she gains mana regen on innate when stealth.
Fizz, Ahri: Oops XD, I have more fav, those 2 are super mobile (Like LB but LB is way too squishy), Ahri has triple flash while Fizz have untargetable and dash. They are neutral in all aspect, because they can be tanky, bursty, mobile to engage or retreat, but not amazing in any aspect. Ahri has a cc but not reliable, fizz has slow which is not reliable too. Ahri has true damage Q, which is good, W for close range, also nice, and a spell vamp innate, though she's mana hungry early. Fizz is prob better, but I just prefer Ahri, because Fizz is simply harder to play.
If ur beignner, play OP like LB, Brand
If ur experience, play Kat, Karthus
If ur long term active addicted fan of LOL, Play Ahri, Diana, Akali, or if u want to challenge, play Talon, Zed (all the Melee base AD champs that are viable for Mid)

If you're looking to try something new, learn Viktor.

Nobody ever plays him, which give you a leg up on the competition. I've even had an edge on hard counters in a couple of games because my lane opponent didn't know what Viktor's abilities are.

Viktor deals TONS of damage, especially late game. His poke is freakin' annoying and his ult will melt anyone without magic resist--and even if it doesn't it will definitely send them out of lane.

I just started playing him a few weeks ago and I LOVE him!