What is the word to describe a person who does not have a personal opinion?

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"