Drawing animate beings
Islam forbids drawing living beings that have souls. These beings are the animals and the humans.
The creation of human or animal animations, paintings or cartoon/anime is not allowed. One should avoid depicting living beings at all times.
The Prophet (peace be upon him) entered my house while there was a curtain with pictures of animals hanging in the house. His face changed in anger and he grabbed hold of the curtain and tore it to pieces. The Prophet (peace and blessings of Allaah be upon him) said: "People who make such images will receive the most severe punishment on the Day of Judgment."
[Sahih al-Bukhari 2225]
Drawing, painting or animating living beings is thus a major sin in Islam. This act is avoided and hated for counterfeiting what Allah has forbidden.
Sa`id bin Abu Al-Hasan reported:
While I was with Ibn 'Abbas, a man came and said, "I earn my livelihood from making images."
Ibn `Abbas said: "I will only tell you what I heard from the Messenger of Allah (ﷺ). I heard him say: "Whoever makes an image will be punished by Allah until he puts life into it, and he will never be able to do that." After hearing this, the man became upset.
Ibn `Abbas then took pity on him and said, "If you insist on making pictures, I advise you to make pictures of trees and other non-living objects."
[Sahih al-Bukhari 2225]
The man earned his income from making images. In the eyes of some he would have strong reason to continue doing so, but Ibn Abbas countered this by following the revelation.
The same also applies to hobbyists who enjoy drawing people or animals. It can feel like a loss, and that is a test from Allah. The Muslim should then give up this hobby, and with the will of Allah this will be rewarded with a great reward.
Salaf Saliheen on drawing animate beings
 أخبرنا عَبْدُ الرَّزَّاقِ، عَنْ مَعْمَرٍ، عَنْ بَعْضِهِمْ، أَنَّ رَجُلًا مِنْ أَصْحَابِ * ابْنِ مَسْعُودٍ نَظَرَ إِلَى رَجُلٍ صَوَّرَ فِي الْأَرْضِ عُصفُورًا فَضَرَبَ يَدَهُ.
كتاب المصنف - عبد الرزاق 
"One of Ibn Mas'oud's friends hit a man on the hand when he saw him drawing a bird on the ground."
[Musannaf Abdurrazzaaq Hadith 20547]
(3) حدثنا أبو بكر قال حدثنا ابن فضيل عن ليث قال: رأيت سالم بن عبد الله متكئا على وسادة حمراء فيها تماثيل فقلت له فقال: إنما يكره هذا لمن ينصبه ويصنعه.
المصنف - ابن أبي شيبة الكوفي - ج ٦ - الصفحة ٨٤
Layth ibn Sa'd reported:
"I saw Salim ibn Abdullah (grandson of Umar ibn al-Khattab) leaning on a red cushion on which there was an image, so I asked him about it. He then told me, 'This is hated for the one who honors objects with images or makes it.""
[Musannaf Ibn Abi Shaybah 6/84]
The Salaf Saliheen owned objects with images on them. They would have these objects in their house and hate curtains and other raised objects with images on them.
It is allowed to have objects with images when they are not honored. For example, carpets, cushions and other objects laying on the floor. Angels will not enter if there are images in the house that are given an honored position (curtains, paintings, figurines, etc).
Omitting the head in drawing animate beings
It is allowed to draw people or animals when the head is omitted. The head is seen as a source of life, so it is not allowed to depict it.
14 أس، فإذا قطع فلا بأس.
المصنف - ابن أبي شيبة الكوفي - ج ٦ - الصفحة ٨٥
"The image of the head is what matters. If that is left out, then there is no problem."
[Musannaf Ibn Abi Shaybah 6/85]