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If you're interested in more than burst, Ryze is actually a pretty good choice. With runes + masteries + 1 25% CDR item or golem buff, you can achieve the cap, which combined with his passive allows him to spam his abilities non-stop.
And nobody mentioned Sion. He has 2 high damage attacks (a shield and a 2 second stun) with 1:1 AP ratios. Combined with Lich Bane, you can achieve a burst of well over 2,000 damage by end game. He's also pretty easy to play (IMO) thanks to high survivability (amazing shield when you stack AP, and great ulti for getting back on your feet) and one of the best stuns in the game.
And really, if you don't care where your magic damage comes from, there are a lot more heroes to choose from. Rammus mostly does magic damage - he may not be a nuker or DPS by definition, but with thornmail, sunfire capes, his ulti and his other abilities, he can drop almost any hero in a few seconds (especially physical DPS), doing almost exclusively magic damage. Then there's Udyr, which, like Jax, does a huge amount of magic damage (Phoenix Stance), or Twitch stacked with attack speed/magical damage items (wit's end, malady, madred's bloodrazor). Katarina with her ulti (does magic damage based on AD). AP shaco (can place 5 boxes doing 400+ damage per hit each, and Two-Shiv Poison at 800+). The list goes on.