Sunfire Cape is a good for Malphite as it offers health and armor to increase his tankiness. The passive AoE burn also supplements his damage and wave clear. It is once again a near mandatory item for Malphite, with its damage increased against champions, this item once again offers everything that Malphite wants, save for mana and CDR.
Iceborn Gauntlet grants armor, mana and CDR which are all useful for Malphite. The bonus damage from the Sheen procs are also good since you will be weaving autoattacks in between abilities anyway due to Brutal Strikes. The ability's free armor also makes Iceborn's slow field huge due to the armor scaling on the item, giving another great source of AoE crowd control.
Randuin's Omen is a very good item for Malphite. It offers attack speed reduction which is really powerful when combined with Malphite's ability to reduce attack speed with his Ground Slam. But more importantly, it protects Malphite from critical strikes, allowing him to become an even more potent ADC counter.
Ninja Tabi are the recommended boots for Malphite in almost any situation. It reinforces Malphite's role as an anti-AD champion since AD champions are often the ones reliant on their basic attacks to do damage. The only situation where Mercury's Treads are recommended is if the enemy team is mostly AP and has lots of crowd control.
Abyssal Mask is your go-to magic resist item as it grants MR, health, cooldown reduction, and mana. The Negatron Cloak in its build path helps against magic damage which is of Malphite's biggest issues. The mana is really useful too because Malphite has high mana costs in general and Eternity lets him restore even more mana. Don't forget of the aura which increase Malphite's damage potential!
Bramble Vest (and by extension Thornmail) makes Malphite almost impossible for most physical damage duelists to deal with him, while at same time countering ADC's lifesteal, while further stacking attack speed reduction with Ground Slam, in addition to providing more damage (due to the extra armor and the passive adding yet another source of damage). All those aspects make Thormail an item that should be heavily considered on Malphite.
While Warmog's Armor does not offer any armor or magic resistance, it is nonetheless Malphite's only source of health sustain, so it can be considered in games where Malphite has to deal with poke or he is constantly getting out of battles with little health. It is also mandatory on ARAM since Malphite cannot to go back to base, as such it is impossible to recover health in any ways other than dying or having a teammate that can heal him.
Gargoyle Stoneplate gives Malphite both armor and magic resistance, and gives him even more resistances when nearby multiple enemies. This makes this item a good choice to consider when the enemy team has lots of both physical and magic damage. The active makes Malphite even tankier, but keep in mind that Malphite then reduces his own damage. And because he lacks good CC outside of his ultimate, his damage is most of Malphite's contribution during teamfights.
Locket of the Iron Solari also offers both magic resistance and armor (it offers more MR than armor however). Its active is a good way to protect your team from damage, especially AoE damage, during teamfights. Malphite can use this item's active to provide an even better follow up for his team when he engages with his ultimate.
Dead Man's Plate gives Malphite better mobility, which is many times very useful, since Malphite is quite immobile outside of his ultimate. However, it lacks the defensive properties of both Randuin's Omen and Thornmail.
Righteous Glory offers Malphite another mobility tool as well as a better way to engage with his ultimate.
Frozen Heart can be considered in lieu of Iceborn Gauntlet (or alongside it, but this isn't recommened since both items offer only armor and no health). While Malphite loses the potential damage and movement speed slow, he gains higher armor, as well as an attack speed slow that stacks with Randuin's Omen or Thornmail, and Ground Slam, for an even stronger attack speed slowing. It can be considered if you prefer to be more durable instead of dealing more damage and having more CC. However, Malphite is often durable enough, and he really appreciates the slow from Iceborn Gauntlet, since he is lacking in CC, unlike other tanks.
Because Malphite has a fantastic 100% AP scaling on Unstoppable Force, and has reliable poke with Seismic Shard, a little of AP can be considered on Malphite. He can also be built with fully AP instead, trading the ability to become a massive tank against physical damage for the ability to murder squishies and potentially deal ridiculous damage in an AoE with his ultimate.
Rod of Ages gives Malphite extra Health, Mana and Ability which will make him a more tanky AP damage dealer.
Luden's Echo offers Malphite everything he wants: Mana, AP and cooldown reduction. This makes this item a nearly mandatory choice on AP builds.
Zhonya's Hourglass is an obvious choice because in addition to having AP, it has armor, and Malphite still scales with armor even with an AP focused build. It has another amazing asset, however: It has an active that saves Malphite's life in many situations and allow him to avoid the following damage once he engages with Unstoppable Force.
Malphite's base damage is high, but the same cannot be said of his AP scalings (except his ultimate). As such, magic penetration items like Haunting Guise, Sorcerer's Shoes, and Void Staff, should be heavily considered.
Being a tank with a kit oriented at countering AD champions, and with a massive armor steroid, the obvious solution is to pick AP champions. They counter Malphite because he is a lot more vulnerable to magic damage. Forcing Malphite to build magic resistance is a detriment to him since his armor scaling spells will do less damage, his armor steroid becomes weaker, and Malphite's kit itself isn't actually suited to deal with AP champions.
Some particular options to deal with him at top lane include:
Vladimir - Probably the biggest counter to Malphite, he can sustain against Malphite's damage, can build a Spirit Visage for further sustain (without reducing his damage since he can gain AP from building HP) or can build a Banshee's Veil which in addition to giving Vladimir magic resistance, will deny Malphite's opportunities to engage. He can get tankier and have more sustain and Malphite can do nothing against that, other than build magic resistance and try to survive a bit more against Vlad, then hope that he can get good engages with his ult later in the game. Keep in mind that Vladimir can avoid being hit by Unstoppable Force with his Sanguine Pool (this is tricky to do, however, since Unstoppable Force has a very high travel speed).
Rumble - He can freely harass Malphite during the lane phase, block Malphite's attempts to poke with his Scrap Shield, and at late game can potentially be as useful during teamfights as Malphite, thanks to his The Equalizer. Malphite can do very little in this matchup because he gets constantly bullied early and is forced to build magic resistance.
Heimerdinger - A very brutal matchup for Malphite because he gets absolutely dominated by Heimer's turrets during the early game. Unlike the other aforementioned matchups, he can't resort to jungler assistance, since Heimerdinger can easily prevent ganks from happening with his turrets.
There are still some AD champions capable of dealing well with Malphite. A notable example is Darius, due to his in-built armor penetration from Apprehend, natural sustain, and overall ability to bully Malphite during the early game. While Malphite can build armor, that armor gets negated by Darius' armor penetration, and also by the true damage from Noxian Guillotine. Darius doesn't really rely on his basic attacks for most of his magic damage so Ground Slam isn't as effective against him as it is against other champions.
Another notable example is Warwick, because he does magic damage even though he is AD. He also has sustain, and has better dueling potential overall.
Most other tanks tend to also do well against Malphite, since they do magic damage and do not have problems itemizing for magic resistance. A notable example is Galio, which unlike Malphite, profits very well from building magic resistance. With his ult, Hero's Entrance, Galio can counter a possible engage from Malphite's team if he uses Unstoppable Force.
Other example is Cho'Gath. He has sustain, better early game waveclear, and even if Malphite builds magic resistance, with Feast, Cho'Gath can deal true damage and execute Malphite if he is low enough on health.
Overall, Malphite should never be blindly picked, since he is easy to counter. If the enemy team has more than one AP champion, Malphtie gets considerably weaker, since not only he is forced to build more magic resistance than usual, but AP compositions tend to have a lot of CC which screws with Malphite's ability to dive the backline.
He wants to be picked into situations where he is favorable. For example, against full AD teams, Malphite does very well, since he is free to stack as much armor as he wants, and ADs tend to not have the tools to stop Malphite from doing his job, like AP champions do. In fact, Malphite is one of the reasons why teams are heavily encouraged to pick at least one AP champion.
Building a The Black Cleaver is a strong option against Malphite, since it reduces his armor. It may sound like an obvious advice, but what isn't initially obvious is that if Malphite's armor is reduced, his spells become weaker, since both Ground Slam and Brutal Strikes scale with his armor.
As an AP champion, building Banshee's Veil can deny Malphite's opportunities to engage with his ultimate. Zhonya's Hourglass can also work in that aspect, with the difference is that you have to time it very well, but with the advantage that you can control when you can use it, unlike Banshee's Veil, which can be poped by another spell.
Unstoppable Force means that you should avoid clumping as a team, since this can make it very easy for Malphite to land a spell on multiple members of your team. Watch out for when Malphite is paired with assassins, however, since assassins can prey on enemies that are distant from each other.
Watch out for AP Malphite. He has a very different playstyle from his tank counterpart. Instead of stacking armor and becoming a massive and durable tank, AP Malphite can nuke enemy champions with his combo, working pretty much like an AP assassin or burst mage. Unstoppable Force has high base damage AND AP ratio, making it an even deadlier spell if Malphite builds AP. When building AP, Malphite actually deals well with some AP champions, since many of them are immobile and have no way to deal with his combo or with his poke potential with Seismic Shard.
However, AP Malphite falls off considerably late game, since unlike actual AP assassins, he can't get out once he engages. He is also significantly squishier, and other than his ultimate, he doesn't actually have good damaging spells. He is a lot more reliant on his ult than his tank counterpart, so if the enemy team manages to play around it, AP Malphite becomes useless.