Using Teleport isn't an every game set, certainly circumstantial, but it does have its place occasionally. Some people might not want to run Flash due to Kassadin's ultimate being, basically, Flash+++, let me tell you that even though that may be the case, Flash is one of the most powerful spells in the game. To have this summoner, and your ultimate makes you so much more deadly in certain situations, and almost impossible to gank to boot.

If you really get to a level of mastery with Kassadin, and you don't feel you're using Kassadin to his full potential with it, it's possible to replace it and run a Silsol Heal/Ignite or perhaps Exhaust. That being said, having an instant double flash is super useful, and annoying for the ones you're playing against.

With the changes to move-speed, as well as the jungle that took place after the Season 3 patch, it is now possible for the use of other starting items now. Even more so if you, for example, used a rune set that included MS quintessences.

I will typically start with set [A1] unless the lane is very difficult, or for some reason I really want the minuscule MS boost the nerfed S3 boots will give. The reason I start with this is so on my first back I can get a Philosophers Stone, Chalice, or Tear. If for some reason I were to judge that the lane would be too difficult, or I would want different items, I would not pick up the charm and either replace with wards or more potions.

When it comes to core/situational builds, it's still pretty early into season 3, so there will most likely be changes as things evolve. For now the core build is typically what I use, and what The Rain Man uses as well. There are times when I/he has gotten a Guardian Angel or Deathfire Grasp but with the changes on the latter item I'm not sure how much better/worse it will be. Overall Kassadin can actually be somewhat flexible with his build, but I really suggest the Rod of Ages at the very least, since you'll be rifting into places/people you'll really need the extra tankiness (it's other stats certainly don't hurt either).

I'm going to be playing around with Archangel's Staff to see if it might be worth it to work into the main build, but for now I'll leave it as situational.

I like to get an early point into Nether Grasp [w] so I can restore some of my mana while farming. It's surprisingly useful for mana regeneration, as well as damage. For the most part said damage will let you last hit better than probably any AP mid's AA, a bit later into the game when your AP is high enough, it also can do large chunks of AA damage to champions. Other than that this is a pretty standard skill order for Kassadin. I've never been in a situation where I wanted to max my Force Pulse [e] first, but it's always an option if you wanted to for some reason.
The only reason I can see to max Nether Grasp [w] before the other abilities would be if you're trolling and doing an on-hit build. Otherwise I would suggest what is above, or something very similar.

To be honest I hate Havoc. I suppose if you output a lot of damage, then by the end of the game you'll have somewhat of a substantial amount of damage boost, but as far as it doing anything noticeable in non-cumulative damage, it just doesn't. If you do a 1000 damage nuke, the mastery, fully powered would only give you an extra 20 damage. Minuscule in my opinion. Thus my extra point in Sorcery/Mental Force, and point in Spellsword. That being said, if you're going to take a point out of anything I would suggest doing so from Mental Force or like I have done, take the point out of Summoner's Wrath. In the long run I would assume the .77 overall damage increase would outdo the 2 AP, and the times you'll have the passive from Wrath up is a bit questionable.

Don't waste points in Butcher Kassadin's Nether Grasp [w] is perfect for farming and it let's you focus points elsewhere, while doing a much more substantial amount of damage.

I wanted to highlight his use of HP Regeneration Quintessences. In conjunction with a Philosopher's Stone, you can easily up your farm in a lane you otherwise could/would be bullied out of. At the start of Season 3 the Philosopher's Stone saw changes to its stats, I would say due to the heavy nerf on HP Regeneration, you could forgo this item and replace the Quintessences with those of Flat AP. It's too early in the season for me to rule it out for good though, it's just my way of saying I can understand why some might question it and not want to use it.

I like the damage that Kassadin is able to put out with having the GP10 item in his inventory, and having it as a first item you should at the very least make your money back from it, and be aided in a small part of the regeneration he needs during the laning phase.

There are a few sets I think are all good, some more situational than others. The runes above are what The Rain Man will typically run on his Kassadin. I do think it is a better set pre-season 3 changes though. With the additions of the new items, the HP regeneration could be replaced with just flat AP, mainly because of the additions of newer items like the Crystalline Flask. That being said, I still personally use the exact set above. The regeneration will actually keep you in lane by itself for quite a while as long as you're not getting harassed beyond belief. I'll try to list a few examples of other usable rune pages below.
Other usable sets of runes include:

Magic Penetration Marks, Health per level Seals, AP per level Glyphs, and Flat AP Quints
Magic Penetration Marks, AP per level Seals, AP per level Glyphs, Flat AP Quints
Magic Penetration Marks, AP per level Seals, Magic Resist Glyphs,Flat AP Quints