PAID Software

iClone

Reallusion's Real-time 3D Animation Software, iClone is great for rapid development and deployment.

Cartoon Animator

Reallusion's latest updated 2D Animation Software gives you professional 2D creativity and animation design.

MOHO (Anime Studio) 

This is my current favourite piece of 2D animation software. More complex to learn than Cartoon Animator, but easier (and cheaper) than ToonBoom Harmony, MOHO (previously Anime Studio) creates professional animations. As a little bonus, you should get 20% off with this link: 20% off MOHO (Anime Studio) animation software.

Toon Boom Animation

I cannot deny that this is THE software used by many of the top animation studios in the world. However, for a hobbyist I feel that the perpetual pricing of this software puts it out of the reach of many. But, if you are more than a hobbyist and want to gain entry into professional animation, then this may be the way you have to go. They do offer a free 21 day trial of the software, which I tried, but gave up on after just a few hours.

Maya Computer Animation & Modelling Software from Autodesk

Maya is supposedly another of the top 3D programmes, offered on a subscription basis, at £1782 per year (13th July '19), a little steep for most hobbyists. However, they do offer a free trial. From their website: Maya® 3D animation, modelling, simulation and rendering software provides an integrated, powerful toolset. Use it for animation, environments, motion graphics, virtual reality and character creation.