There will be no spitting in Paradise.
Spitting to your left side is a way to be safe from a bad dream.
Spitting to your left three times stops the interference of Satan.
Muhammad spat on people and objects to bless them.
Narrated Mahmud bin Ar-Rabi': I remember Allah's Apostle and also the mouthful of water
which he took from a bucket in our house and ejected (on me). ...
(Sahih Bukhari: volume 1, book 12,
number 801)
... Urwa returned to his people and said, "O people! By Allah, I have been to the kings
and to Caesar, Khosrau and An-Najashi, yet I have never seen any of them respected by his
courtiers as much as Muhammad is respected by his companions. By Allah, if he spat,
the spittle would fall in the hand of one of them (i.e. the Prophet's companions) who would
rub it on his face and skin; if he ordered them, they would carry out his order immediately;
if he performed ablution, they would struggle to take the remaining water ... (Sahih al-Bukhari: volume 3, book 50,
number 891)
Narrated Jabir bin 'Abdullah: ... So I came (to my house) and Allah's Apostle too,
came, proceeding before the people. When I came to my wife, she said, "May Allah do
so-and-so to you." I said, "I have told the Prophet of what you said." Then she brought out
to him (i.e. the Prophet) the dough, and he spat in it and invoked for Allah's Blessings
in it. Then he proceeded towards our earthenware meat-pot and spat in it and invoked
for Allah's Blessings in it. (Sahih al-Bukhari: volume 5, book 59,
number 428)
Muhammad spat in Ali's eyes to bless them, (Sahih al-Bukhari: volume 4, book 52,
number 192)
Muhammad spat in a well to bless it, (Sahih al-Bukhari: volume 5, book 59,
number 472)
Related to Muhammad spitting on people is the reverence that was given to his used ablution water.