@Umlaaat:
Video / showreel always works much better than sending just music files. This is because with a video you're demonstrating your ability to write music which fits and/or augments the mood of the game.
Friendly tip 1:
Resist the urge to write epic cinematic orchestral battle music (รก la Hans Zimmer) with East West libraries and putting it as the first song on your demo list. Lots of eager-to-be game musicians send their demos to our company and 99% of them always do the above, so I would imagine they're doing it when they're sending their demos to other companies aswell. I'm usually the one listening to the demos we get and if there's a mediocre Hans Zimmer battle scene copy as the first song, I usually skip the rest of the songs. This is because almost always rest of the songs are also in the similar lines as the first one, including the quality of the music.
Friendly tip 2:
Be diverse. This is really important for getting work in the gaming industry. Developers are usually the ones hiring the audio guys for their projects and they don't like hunting for the talent all the time. If they know someone who can come up with almost any kind of music, the devs are likely to use that person regularly for their projects. Especially if the results always end up being really good.
Friendly tip 3:
The demo song compositions AND productions need to be top notch. They have to sound professional in all aspects. Game developers aren't interested in working as a music producer who hires the composer, engineer, session players, mixing engineer, etc. You will be the one doing all those tasks either all by yourself or by hiring extra talent for the project. Since the budgets for the audio usually aren't very big, creating the music is usually a one or two man show. You most likely need to learn how to do it all.
About the demo video:
Make sure you demonstrate the quality and diversity you can provide for the client. Also make sure the songs fit the video material's mood. As an example, here's the demo reel from the sound guy we usually use for our projects: