What is the word to describe a person who does not have a personal opinion or stand on a subject?
If somebody says X is right, then you could agree. But if some other person says X is wrong, and you also agree, you are not really expressing your own opinion. You are simply agreeing with everyone else. How do you describe that kind of personality with one word in a formal way? Specifically, someone who cannot make decisions on their own and depends on others' opinions.
One who doesn't take a stance on a subject can be characterized as impartial or indifferent
impartial (adj) - treating all rivals or disputants equally; fair and just:
indifferent (adj) - having no particular interest or sympathy; unconcerned*
One who can't make decisions on his own is certainly diffident:
adj - lacking confidence in one's own ability, worth, or fitness; timid; shy.
There are many options though. You should be more specific and maybe provide some context: apathetic, infirm, weak-willed, detached, aloof are all terms that spring to mind.
Medically speaking, a person who can't make his own decisions and constantly depends on others suffers from Dependent Personality Disorder.
New Oxford American Dictionary*
Some of the following nouns and adjectives may apply.
• wishy-washy, “Wavering; lacking in commitment, certainty, or support; namby-pamby.”
• yes man (or yes-man), “(idiomatic) A person who always agrees with his employer or superior.”
• yeasayer, “(pejorative) One who habitually agrees uncritically.”
• weathercock, “(figuratively) One who veers with every change of current opinion; a fickle, inconstant person.”
• fickle, “Quick to change one’s opinion or allegiance; insincere; not loyal or reliable.”
Consider meek.
meek: evidencing little spirit or courage; overly submissive or compliant
That person is a sheep.
a person who is too easily influenced or led.
"the party members had become sheep, and she refused to be taken in"
I would say that this person is agreeable
