Bettas got their nickname "fighting fish" due to their highly territorial and aggressive nature. Never house two male bettas together. Because they are confined to a tank, they will often fight to the death. A male and female housed together will attempt to mate. One will aggressively chase the other, which can result in death.

It's best to keep bettas alone, but if you want to add tank-mates, choose a peaceful, tropical fish, with short fins and dull color. This is to ensure the betta does not mistake a long-finned, colorful guppy for another betta.

When considering tank-mates, keep in mind that the betta should be added to an established tank, not the other way around.
This is to prevent the betta from feeling like his territory is being invaded.
Also consider that not every betta will tolerate tank-mates at all.
I have a female that won't tolerate other fish, shrimp, or even snails!

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Tank-mates

Below is a list of common tank-mates. Please research the species thoroughly before buying.
Note: Many common tank-mates are schooling fish, so you have to get more then one.
This means you'll need a big enough tank to house everyone happily.

Harlequin Rasbora
How Many: 6+
Min Tank: 15 gallon

Ember Tetra
How Many: 7+
Min Tank: 10 gallon

Pleco ~ bristlenose & clown
How Many: 1
Min Tank: 20 gallon

Kuhli Loach
How Many: 4+
Min Tank: 20 gallon

Amano Shrimp
How Many: 2+
Min Tank: 5 gallon

Snail ~ all varieties
How Many: any
Min Tank: 5-10 gallon

Oto Catfish
How Many: 3+
Min Tank: 10 gallon

Cory Catfish ~ pygmy, albino, etc.
How Many: 5+
Min Tank: 20 gallon

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Sororities

Sororities are a single tank with 5 or more female bettas living together.

...and they are a huge controversy in the betta fish community.
Many believe they are stressful for the fish and will inevitably end in disaster.
Yet many still, have kept sororities with great success.
Success comes down to multiple factors: personality of the fish, tank size, plant coverage, and careful introduction.

Personality

Each betta is different.
Some are highly territorial and moody; always on guard and aggressive to any living being in their tank. They cannot handle tank-mates of any kind, much less another betta. Some are so passive they will tolerate anyone. Then there's everything in-between. You must get to know your fish and introduce it to non-betta tank-mates to evaluate its aggression.

Tank Size

Each female should have around 3-5 gallons to herself within the tank. If they are packed into a small space, territorial disputes will eventually break out. Bettas are not social creatures, and prefer plenty of time in solitude. A successful sorority will see females coexisting without stress.

Plant Coverage

A heavily planted/decorated tank will disrupt the line of sight, keeping aggression and stress down. Each female should have her own hide, spaced apart, and separated by plant coverage.

Careful Introduction

To create a successfully sorority, the females must be introduced to the new tank all at once. They will spend the first few days establishing a hierarchy and setting boundaries, then much of the aggression should stop. If it doesn't stop or gets worse, it must be reset, with the aggressive one(s) removed.

The problem is that even if you do everything right, the sorority can fail.
I believe they should only be attempted by experienced fish-keepers, who know their fish very well, can identify the signs of stress and aggression, and have the resources to intervene and remove all the females if a problem occurs.