Beginnings
Every beginning is difficult.
When I started with YouTube three years ago, I was using Canon PowerShot SX130 IS - really great universal pocket camera that was capable of shooting videos at HD (720p) with pretty fast autofocus.
Video quality was quite good but quality of sound was bad, it was not possible to connect external mic and camera did not provide much options for video settings.
Anyway, I was not bothered with it at all - I just shooted for fun and did not really care about the quality.
I recommend same to you - if you want to start on YouTube but don't have great equipment, it should not hold you back - just start shooting and if you will have interesting content, you will find your audience anyway and you can improve your gear over the time.
Current equipment
Most important part of the gear is of course camera.
I use Canon 700D with 18-135 mm IS STM lens.
I'm happy with video quality and settings options that this camera can provide - it is great camera for universal use.
Only thing that is not so great is sound quality so I use external microphone - Rode Smartlav+.
This microphone was originally designed to be connected to smartphone but with cheap reduction it can be connected to any camera as well.
For long time I did not care about post processing - I was simply ignoring all options of editing software, I just put videos together with few transitions between each part.
This was a big mistake and I learned that good post processing can greatly improve video quality.
For this I use Adobe Premiere Elements 12 that I luckily received for free with my camera - it its simple editing software but provides many usefull options for post processing....
So this is basically my current equipment. I also use tripod but its not so important part of the gear - any tripod would do the job :)
In general I don't think you need such equipment for shooting type of videos I shoot - card tricks, magic and playing cards reviews.
I purchased all of this mainly not because of YouTube but for other reason.
The most important thing will always be content of your videos.
What equipment are you currently using and what would you like to improve on it? - Let me know in comments below.