I had hoped that the SQL improvements would fix this annoyance, but according to the documentation they did not:

  create table fib ( a integer, b integer );
  insert into fib (a, b) values (1, 0);
  update fib set a=a+b, b=a;
  update fib set a=a+b, b=a;
  update fib set a=a+b, b=a;
  update fib set a=a+b, b=a;
  update fib set a=a+b, b=a;
  select a, b from fib;

The correct result according to the SQL standard is a == 8 and b == 5. In MySQL the result is a == 16 and b == 16. They do document this in the manual, saying UPDATE evaluates the assignments left to write, and note that this deviates from the standard.

MariaDB is the same prior to 10.3.5. Starting with 10.3.5 it defaults to left to write evaluation, but you can set the SIMULTANEOUS_ASSIGNMENT mode flag to make UPDATE evaluate the assignments simultaneously instead of left to right.

I believe that all other common SQL databases (Sqlite, PostgreSQL, Oracle, Microsoft SQL Server) follow the standard.