(Other than 'Captain Atom', who was the inspiration
behind the Watchmen character,and was one of the
characters who were originally to be featured
in the comic series)
Dr. Manhattan is easily one
of the most powerful comic/movie superheroes or
characters in general, having almost godlike
abilities.

However, in science-fiction generally, these
abilities are hardly without precedent and in
fact Dr. Manhattan has quite a few limitations,
being: he cannot actually fly or predict the
future in general terms, although he does appear
to; similarly,he is not actually telepathic and
only possesses limited telekinetic abilities.
His 'powers' are also limited to objects in his
own line of sight or at least in close proximity.

All the following characters or types posses one
or more of the above 'powers':
A 'Mind' or vessel etc containing an 'Effector'
(Culture novels)
Paul Atredies (Dune saga)
Any sufficiently powerful telepath or telekinetic;
i.e. Jedi Master, Sith Lord, (above) P13 (Babylon 5),
Cthulhu and, arguably, Q (Star Trek:TNG,DS9 and VGR)

The last two, arguably, have beyond godlike powers as
they apparently consist of exotic matter and so presumably
would be (mostly) immune to Dr. Manhattan's abilities.

Dr. Manhattan's apparent precognitive abilities are
'merely' a form of deja vu; he apparently has access
to all his memories simultaneously: past, present and
future.

His main abilities concern the manipulation of the
quantum mechanical wave function of himself or any
object in his line of sight, presumably following
the Observer Principle. Arguably, a civilisation
such as the Culture or the Monolith Builders
(Odyssey saga)
would have greater power.

Any conflict between beings with godlike or near
godlike powers could be resolved on the assumption
that one godlike being has a high probability
of being defeated by two others, of the same or
different type.

It should be finally added that Dr. Manhattan
cannot become invisible, access parallel or
higher dimensions personally, travel back in time
or,technically, travel faster than the speed of light.