Time for another installment of "Who Are These Aliens Anyway" with background about more of our enemies. See
this post for the previous installment.
Already encountered (although only once so far) are:
Cyberdisks (minor type, serve Sectoids)
These terror units appear along with their Sectoid masters during terror missions (where we recently encounted them for the first time), base assaults, base defense, and with battleship and terror ship missions. The Cyberdisk is a large (4 tile) flat disk of alien machinery which moves by alien anti-grav technology.
Cyberdisks can be fearsome opponents as they are armored (taking 20% less damage from armor-piercing weapons and 40% less damage from HE), fast moving, fly, and mount a powerful plasma beam weapon that can kill even a heavily armored solider with one shot. As if that wasn't bad enough, Cyberdisks have an automatic self-destruct which causes a massive explosion stronger than an alien grenade and covering a significant area. Any XCOM soldier who turns a corner or goes through a door and finds themselves facing a Cyberdisk at close range will be extraordinarily lucky to escape with no worse than serious wounds.
The Cyberdisk self-destruct can be used against the aliens, however, as the hovering disks often accompany their masters closely. I once killed a Cyberdisk from a distance with a heavy plasma, and the self-destruct killed two other Cyberdisks; they then self-destructed and wiped out four Sectoids I had not even seen. Seven at one blow!

While that kind of chain reaction is rare, it is not uncommon to catch a Sectoid or two a little too close to their terror weapons.
XCOM hovertanks (which we have not yet researched/built) are largely inspired by the Cyberdisk.
Not yet encountered in game but very likely to show up at any time are:
Snakemen (major type)
The third major alien type threatening the Earth is the Snakeman. Reptilian and scaly, the Snakeman looks like an abbreviated torso and head on top of a sinuous, muscular body which serves as the "foot" supporting and propelling the creature. The extremely tough hide is golden brown.
Snakemen are tougher opponents in combat than Sectoids or Floaters, being harder to kill and also more skilled with weapons (both firing and throwing). They are quite resistant to fire (30% less damage than normal). Their biggest weakness is lack of speed: their slithering motion does not cover ground very rapidly.
Snakemen do not possess Psi powers.
Chryssalids (minor type, serve Snakemen)
The Snakemen's servants are in most people's minds far more terrifying than their masters. Some consider them the most terrifying of all the aliens threatening Earth...even more so than the Psi users.
Chryssalids are bipedal, insect-like creatures with a shiny blue-ish exoskeleton and huge claws. (Unlike most terror units, Chryssalids occupy only 1 tile.)
Chryssalids have tremendous speed, and are capable of running from beyond visual range (20 tiles) to attack with their claws in a single turn. The Chryssalid's claw melee attack can do a lot of damage, but unless attacking a tank does not really matter. The true danger of the Chryssalid is that any living human it attacks -- even if it misses and does no damage! -- is injected with an egg and becomes a zombie. (See below) Armor does not prevent this, and at the beginning of the next round the victim is transformed. And when the zombie is killed, a new Chryssalid hatches from the remains!
It is possible for a Chryssalid to zombify multiple humans in a turn. So if even a single Chryssalid gets in amongst your soldiers, especially early when they are grouped in and around the Skyranger...entire teams can be wiped out almost before you can realize what is happening.
The best defense against Chryssalids is to stay out of their reach. Soldiers in Flying Suits can rise off the ground and the Chryssalid can do nothing but shriek angrily. But be careful to stay in open air -- if a flying soldier is next to a window or staircase Chryssalids can still reach them and even a Flying Suit is no protection from being turned into a zombie.
Note that Snakeman/Chryssalid terror missions can be especially terrifying, as the Chryssalids can zombify all those wandering citizens XCOM is supposed to be saving.

The points penalties are large, but some recommend shooting any citizen you see during such a terror mission.
Zombies (minor type, created by Chryssalids)
Zombies are the shambling, dissolving remains of a human injected with an egg by a Chryssalid. Poor bastards.
Zombies generally only have a melee attack (sometimes one can spawn with the weapons of the original human host, but they will only use them for reaction shots), but are capable of delivering quite a blow...if they can get close enough. These are slow zombies, fortunately.
The critical danger of a zombie is that it is also a new Chryssalid in waiting, ready to pop out and attack as soon as the zombie is struck down. This can be a real problem if the zombie is killed by reaction fire, as the new Chryssalid can move and attack in the same alien phase.
If possible, zombies should only be killed when multiple soldiers are present to combine firepower on the new Chryssalid and immediately kill it as well. If not enough soldiers or TUs are available for the task, running away until support can arrive may be the best option.
More alien types will be discussed later, once they show up in game.