How old is Anakin/Darth Vader supposed to be in each of the movies?

Hello skipw719-ga

Thank-you for your question.

According to the Star Wars Databank at the excellent starwars.com
website, Anakin Skywalker is 9 years old in Episode 1.  From the
official timeline published by Random House (who publish the Star Wars
books) we can also determine when each movie took place and
extrapolate his age.

Phantom Menace took place 32 years before Star Wars Episode 4; Attack
of the Clones took place 22 years before Episode 4; Revenge of the
Sith took place 19 years before Episode 4; Empire Strikes Back took
place 3 years after Episode 4 and Return of the Jedi took place 4
years after Episode 4.

Applying this to our knowledge of Anakin being 9 in Phantom Menace we
can conlude that he was these ages in each film:

Phantom Menace        9 years old
Attack of the Clones 19 years old
Revenge of the Sith  22 years old
A New Hope           41 years old
Empire Strikes Back  44 years old
Return of the Jedi   45 years old

These ages can be verified using these pages:
http://www.starwars.com/databank/character/anakinskywalker/
http://www.randomhouse.com/delrey/starwars/timeline.html

The actor who played Anakin in the first movie was Jake Lloyd who was
born on March 5 1989.  This made him approximately 9 years old when he
was making the movie (as the movie was released in 1999 but in
post-production for at least a year).

If you require any further information please do not heistate to ask
for clarification.

I'll make a stab at it to start a discussion of people who know more than me :)

Episode      Age
  1           8
  2          18
  3          21
  4          40
  5          43
  6          44

Based on looks of the actors involved and any timeline clues I could conjur up.

According to Weird Al in "The Saga Begins", he is 9 in Episode 1:
http://www.azlyrics.com/lyrics/weirdalyankovic/thesagabegins.html

I will yield to the omnipotence of Weird Al.  Add 1 to every one of my
answers.  But I'll ask, does anyone know the age of the actor who
played Ani in Episode 1?  I'd guess he was 7, but that doesn't seem to
fit with his character (9 or 10 does seem to fit his character
better)... I took the average and guessed 8 (if you cared about my
logic at all).

9
19
22
41
44
45

Trading cards that came out at the time of Episode 5 listed Darth
Vader's age as either 56 or 57 (I cannot recall which). I wish I still
had one for proof, but can say that I was playing Darth for a
children's camp group in the summer of 1980 and I went in to the Post
Office on a lark to pick up stamps-- in costume, and with my other
performers; a princess, GI Joe, and a few others.

I noticed the Selective Service registration form and asked if I
should fill one out. The clerk told me the age range was 18 to (I
think) 35 and I replied that I, Darth, was too old. As proof, I
produced the aforementioned trading card.

Ten minutes later we stopped in a convenience store for sodas where
the clerk thought he was being robbed and activated the silent alarm.
We paid for our items and left only to be stopped a dozen feet from
the store entrance by three cop cars, fully half the town's police
force.

After a few tense minutes, the cops sorted it all out. As we had done
nothing wrong, I was furious with the clerk and insisted he be
arrested for a range of crimes (I included allegations that his mother
had not been married to his father at the time of his birth, but
worded it a bit more succintly) but we settled for an apology.

Um, I seem to have strayed a bit. Sorry.