Thanos is above manual labor

As much as he gets his own hands "dirty" (during the flashback), in the previous films (Avengers, Guardians of the Galaxy) he's been more than happy to let someone else (try) to do the work for him.
If he has to do it, he may as well get it over and done with quickly.

The complete set is enticing

As shown in Avengers: Infinity Wars, Thanos seems to be taking his army planet-to-planet to do the 50/50 thing.

Each additional infinity stone would be a dramatic boost to his efforts, but if he gets all of them, he can get it done quickly.

A drawn out campaign leaves room for error

Considering how close they got to stopping him when he didn't have all of the stones, if he was content with two or three stones, his plan could be stopped much sooner than he wanted.

Each stone is only a part of the universe

Demonstrated throughout the films, each stone seems to be really, really good at its one job. When used together with others, it's plausible that its effect can be exponentially increased.

Discussing it with friends, we seem to pin it more towards what the extent of the power of each gem might be.

• Power: power the other stones to
  the other gems seem to have localized effects, this might help them expand
• Reality: do what he wants
• Time: instantly
  increases the speed at which the other gems take effect - snap of fingers
• Space: everywhere
  bridging space across the universe is its job, but usually point-to-point
• Mind: targeting everyone
  Increases mental power/elevates mind - gives him the mental faculty to affect the entire universe
• Soul: fairly
  "A soul for a soul" sounds like a fair trade, also the wiki says dominion over life and death

I like Skibisky's thoughts, that perhaps each stone plays its own role.

Here's what I think they may be doing if this were the case:

Enact his will to fairly — Mind
manipulate energy — Power
everywhere across the universe — Space
wiping from existence — Reality
only sentient beings — Soul
immediately (and irreversibly?). — Time

I believe power has to be used to cause that disintegration, that's what I mean by "manipulate energy". Matter is a form of energy, organisms are made from matter — maybe the matter they are made of is being destroyed (thought impossible under conventional laws of physics). Or the energy binding them together is being manipulated.

I don't actually think each stone fulfils a specific purpose like this though, I think it's simply that the change he wants to make is so large-scale that he needs to be able to manipulate the entire cosmos at once. Only all the stones brought together can do this.

You suggest he use the time stone to "freeze" time as he journeys the universe killing people.

I wonder if Thanos is worried he would get bored of this and lose his will to commit this genocide, or become mad in old-age (perhaps not physical but his mind would be ageing).

Also, we have seen that the time stone seems to only work locally when used in isolation from the other stones.

I think to alter the fabric of the universe, to make such massive changes on such a large scale, he truly needs all of the stones to work together, like they did when the universe was created.

When Wong is explaining the Infinity Stones to Bruce at the start of the Avengers: Infinity War he mentions that when the universe began the infinity stones each represented a core aspect of the universe: Reality, Time, Space, Soul, Power and Mind. In order for Thanos to carry out his plan on a universal scale, it stands to reason that he would need to be in full control of every element of the Universe to effectively make him 'Master of the Universe'

All the other answers seem to miss the most important detail as to why Thanos wanted all Infinity Stones.

Thanos himself gave the answer. It was mercy.

When Thanos meets Dr. Strange, he shows his home Titan through reality stone.

Thanos: It was once beautiful like any other planet but there were more mouths to feed than resources. So I suggested a plan.
Strange: Genocide.
Thanos: Yes, but random, fair to the rich & poor.
Strange: You're a murderer.
Thanos: I am a survivor. I intend to replicate that throughout the universe. And with all the Infinity Stones, I could do that with a snap of my fingers. I would call that mercy.

Quotes aren't totally accurate but that's what he said.

Using all the Infinity Stones, he could kill half the population of the universe with a snap. Nobody would feel pain & it would be merciful death.

For Thanos to correctly and fully use the power of the gauntlet he needed all six of the stones to carry out his plan (to kill half the universe's population at the snap of his fingers**). The gauntlet was made by Eitri of Nidavellir – home of the dwarves. Eitri reveals that Thanos invaded and forced him to create the Infinity Gauntlet just for this purpose.

Also, the Infinity Stones seem to be linked together, so when doing something of the magnitude that Thanos was doing, the whole six were needed.

According to how the powers of the stones were shown in the movies, it seems that each individual stone is only able to impact a local space rather than a universal space when used separately.

This is most notably seen in when the reality stone was used. When Thanos transformed Drax and Mantis into different objects, they promptly returned to normal after Thanos warped out of the local space. This means that if Thanos used the powers of the glove to erase life from each local region using the powers of the stones, it would be undone as soon as he left unless he killed them using his army by hand. To kill half the life forms of the universe by hand would probably be too slow to to make an impact as the growth rate of life forms is probably way faster than he can wipe them out. So in summary, he needs all of the stones so:

1. his work would not be undone once he left the local space
2. expedite the work to a point that is impactful on a universal scale

Thanos needed all six stones in order to complete his goal... It's his goal that seems to be misunderstood here.

I agree with others above that all the stones are powerful but become even more so when used together, therefore

The MCU (I'm not including the comics) has gone to great lengths to show that Thanos believes himself to be doing the right thing on the grand universal scale.

He didn't seem to want to go around killing off half the population of every planet, in his mind he was going round and saving each planet from itself but he knew that he would then need to either leave some of his forces there to continue to monitor this or return every few hundred years after each planet would have a population boom, all six stones gives him the ability to immediately get what he wants but also have this effect continue for all time, therefore... again in his mind protecting the entire universe from the beings that call it home while this hasn't been shown in the MCU it stands to reason that would be his end goal given what we know about him

He's shown he is capable of Love as well as compassion (Gamora in both cases) as well as respect (Stark) he also shown he can be honourable, by keeping his word to Dr Strange in keeping stark alive. He explains to Gamora that her homeworld lives happy "balanced" lives,

This all points to him thinking he is doing the right thing... maybe the clinically insance genocidal thing, but he obviously believes the needs of the many outweigh the needs of the few.

When you keep this in mind it makes sense that without each and every stone, he would never be able to achieve his ultimate universal goal

Consider the size of the universe. Thanos wanted to enact his plan on every single populated planet in the universe.

He was powerful enough to enact his plan on any planet he wanted, as seen by the fact that he killed half the population on Drax's and Gamora's home planets. However, doing this to a planet takes time. No matter how powerful he is, even with any 5 of the 6 stones, he has to spend some amount of time killing the population of a single planet.

Imagine that he was so powerful that he could do this at a rate of 1 planet per minute; using the space stone to travel from planet to planet. There are an estimated 1,000,000,000,000,000,000,000 stars in the observable universe. If we assume that there is one inhabited planet for every one million stars (random guess / figure there); then it would take him 1,902,587,519 years to carry out his plan. That's if he literally went around killing people non-stop for that whole time. And that's just the observable universe; not the entire universe.

With all 6 Infinity Stones; he would be able to accomplish that entire task instantly. So even if it took him thousands of years to collect the 6 stones; that would still be more efficient than doing it without them.

Thanos’ goal was to irreversibly kill exactly half of all life across the universe, indiscriminately, and without causing the dead any pain or suffering. In order to do this, he would have to have the power to locate all living things, select exactly half at random, make them insensitive to pain, and disintegrate their matter—ideally, in a way that could not be undone. As such, each of the Infinity Stones is likely given the following tasks:

• Soul – Locate all living things; kill those selected
• Mind – Select those to be killed evenly; anesthetize those killed
• Power – Provide the energy necessary to disintegrate all those organisms
• Reality – Manipulate the organisms to disintegrate without leaving any remains
• Space – Allow this to happen simultaneously and on a universal scale
• Time – Make the deed instant and irreversible otherwise