Is Godzilla the good guy in his movies?

A bit of both
1954-1955 During this period Godzilla appears. These movies are
written in the light of showing the horror of Nuclear
radiation/warfare and have a very sober effect.

1962-1964 This period ignores the 1954-1955 time period, consisting of
movies where Godzilla is seen as a evil menace (winner or loser)
fighting other monsters.

1964-1975 This period disregards all previous periods. Commonly know
as the "Godzilla vs. Monster X" period, this time span consists
entirely of formula movies. In the better part of these movies,
Godzilla, with or without the help of one of his friends, beats the
tar out of a monster invading earth (frequently controlled by space
aliens). These movies are the true classics (aside from the first), a
bit cheesy, but fun to watch once you accept the lack or realism.

http://godzilla.monstrous.com/godzilla_s_life.htm

GOdzilla is the typical anti-hero. He not only embodies the fears of
Nuclear Holocaust (thereby evil), but he always defends humans against
"natural monsters" (thereby good). He would be along the same sort of
lines as Wolverine in the "X-men" comic book series. He'll save the
day, but he aint a do-gooder.

One Godzilla site I recall said that the Godzilla you see in all the
movies may not even be the same Godzilla all throughout. The original
Gojira in the very first movie was actually destroyed (as was the
Godzilla in Godzilla vs. Destoroyah). I think after the first
Godzilla, the second one fights Mothra and others, Godzilla 1985 is
the third, the fourth I believe is the one dying in Godzilla vs.
Destoroyah (or maybe the same as the third), then Godzilla 2000 is the
newest.

The big guy definitely goes both ways.

Because of the fact that Godzilla is an animal and because the series
suffers from some King Kong envy at times, even when Godzilla is a
feared and deadly monster as in these films:
http://www.filmjudge.ca/g/godzillatokyosos.htm
http://www.filmjudge.ca/g/godzillavsmechagodzilla2.htm
http://www.filmjudge.ca/g/godzillavsmechagodzilla.htm
Someone (usually a woman or child, but sometimes the sensitive male
hero or older person) will mourn or fear his death.

In other films he is a more straight forward good-guy, or at least a
tool the good guys use to defeat a very bad monster before Godzilla
leaves peacefully:
http://www.filmjudge.ca/g/godzillavsgigan.htm
http://www.filmjudge.ca/g/godzillavsseamonster.htm
and
http://www.filmjudge.ca/g/godzillavshedorah.htm

When Godzilla leans toward badguy status, Mothra is usually there to
be the good guy, flapping his dusty wings and flying around until
Godzilla is subdued.

In any case, if you like Godzilla movies, you cheer for the big guy no
matter what, because even when Godzilla wreaks havoc on Tokyo (and
surrounding wastelands with their one or two papier mache buildings -
depending on the quality of the particular flick) it is usually for a
"good reason" - like the humans have invented something terrible,
experimented with something terrible or some terrible monsters either
from Earth or Space demand that Godzilla smash everything in sight.

Ultimately, Godzilla is beyond good or evil, Godzilla is simply the
equalizing force of nature.  It's all about balance.  It's an Asian
thing.