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Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 6 such that the first six numbers are as listed in the question followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
In this particular example, the simplest solution, based on a polynomial or order 5, is
t(n) = (6n^5 - 125n^4 + 920n^3 - 2995n^2 + 4474n - 2280)/120 for n = 1, 2, 3, ...
and, accordingly, the next term is -12.
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What comes next 1 2 3 0 -1?
The next term is -2.
What number comes next 0 1 4 9?
16' then 25 and then 36 et.seq. The clue is 0,1,4,9,16,25,36, ... = 0^(2) , 1(2) , 2^(2), 3^(2) , 4^(2) , 5^(2) , 6^(2), ... n^(2) ...
What number comes before 1 2?
It is: 0 1 2 3 ... etc
What comes next b 0 c 2 d 0 e 3 f 3 g?
4
What is the next number in the sequence 1 2 3 4 0 1 2 3 1 0 1?
12110 0r 1210
