I often hear people begin a sentence with "Wonder if ..." when I think
they should said "I wonder if ..." or "What if ..."  Is "Wonder if
..." proper?

Though not grammatically correct, this form of slang has permeated the
vernacular of nearly all native English speakers. The reason for this
is the fact that there is no subject, rather it is implied, and unless
the speaker is using an imperitive form, also an incorrect syntax when
"wonder if" is involved, this usage is not proper.  The part missing
is the often implied "do you" or "I" preceeding "wonder if".  Also you
might be wondering why I said there is no subject even if the sentence
were "Wonder if pigs can fly."  Misleading as it might be "pigs" is
not the subject.  This is due to the fact that "if" is a subordinating
conjunction signaling the beginning of a subordinate clause in which
"pigs" is the subject.  (still following me?)  As a rule, subordinate
clasues cannot stand alone (imagine the confusion of just saying "If
pigs can fly")  Therefore, the only part of the independent clause is
wonder, and as said earlier, considering the syntax 'you' cannot be
implied for it is not an imperitive (directive) sentence.  A correct
way of expressing this thought would be to say "Do you wonder if..."
or as you suggested "I wonder if.."  Also correct would be "What
if..." since in this case "what" is an interrogative pronoun, and
therefore can act as a subject of the sentence.

Hope I helped
Mike
10th grade English student

Burfart is pretty much right-- it is only a correct statement if used
as an imperative (command form, with "you" as the implied subject). If
you are using it in the sense of "Think about this..." then it could
actually be ok. But in general it is ugly slang.

I forgot to mention, what is even liable for grammatical error is the
word "if." "If" implies an "if,then" function, like "I wonder if you
fell from 30 feet, (then) would you die?" But more often than not,
people use "wonder" in the sense of a "whether or not" function, e.g.,
"I wonder whether moldy bread is poisonous (or not)," in which case
"if" would be a grammatically incorrect word.

At first I thought this was a strange question, because I have never
noticed people doing this.  Then I started saying it to see which
sounded right, and realized that even though I say "I wonder if...",
the "I" often comes out softly and blends into the beginning of the
word "wonder," so that if you weren't listening closely (as you might
not be right at the start of someone else talking), you would miss the
word "I", even though I said it.  I wonder if this is what you are
hearing, or not hearing as the case may be.  I certainly don't see the
"I" left off in writing, so people know it belongs there.

The thing that I notice in the written form of this statement is that
a lot of people put a question mark at the end, as in, "I wonder if
pigs can fly?"  This of course, is incorrect, as the sentence is a
statement of my own wonder, not a question.

Of course, the English language is not a static entity, but is
constantly evolving, so what is correct now will not necessarily stay
correct, nor does it follow the same rules in all countries.  The
purpose of language is to communicate, and I much prefer incorrect
grammar which communicates a message clearly to perfect polished
language which is used to obfuscate or confuse.

Wonder if you'll get an answer....?

Starting a sentence with "wonder if" is incorrect.  Every sentence in
the English Language needs a subject (a person or thing that is
performing an action)and a predicate (or verb...this is the action
that the subject is performing).  If someone said "Wonder if he is
nice," the word "wonder" would be the predicate, but there would be no
subject.  In other words, there wouldn't be anyone wondering in a
sentence starting with "wonder if".  One has to state "I wonder" or
"he wonders" or "you wonder" (etc.) before he continues his sentence.

It might be appropriate if you are tring to get any kind of discussion
under way, as the listeners could appropiately respond to any one as
the subject, thus broadening the possibilties, including an analysis
of why it is bad grammer.   Neil

Strictly speaking, yes, to begin a sentence "Wonder if..." would be
incorrect, since no subject is present. But the thing about language
is that it's incredibly flexible, and in general we can think of
"language" as being successful if the correct meaning is conveyed
unambiguously. In this case it's clear that the intended subject of
the sentence is "I". So as long as we're reasonably assured that the
listener will assume the implied subject, we can't really take issue
with whether this sentence succeeds in conveying its meaning.
Stylistically we might make criticisms, but in conversational language
style is not necessarily a primary consideration.

This situation is similar to someone saying, "May I leave the table?"
and the head of the table replying, "You may." The head of the table
doesn't say what the person may do, but it's clear what is intended.
"You may" on its own is essentially meaningless--you may do what? Eat
an elephant? Grow antennae? Pitch a no-hitter? But in its context
there is no ambiguity to the meaning of the utterance, so the language
does what it was intended: it indicates to the listener that they may,
in fact, leave the table.

Another way it was put to me once is this: Let's say I find a sticky
note on the fridge that says:

S- 
GET LAUNDRY
-A

From a grammatical-stylistic point of view, this is an abomination.
There is a lack of punctuation and articles, capitalization is used
incorrectly, as are seemingly arbitrary abbreviations, etc. But in the
note's context as "a note left for me on the fridge" the meaning is
clear: A. (let's say Alice) wants me (Smudgy) to get the laundry. In
this sense the communication is entirely successful, and perhaps even
close to ideal: it conveys its meaning within its context and with a
minimum of superfluous material.

In short, since "Wonder if..." is clearly from a casual context and
not a formal one, and since it generally conveys its meaning clearly
and entirley, it's churlish even to attempt to criticize it on
stylistic grounds.

As for why this phenomenon occurs, I imagine it has to do with the
fact that sometimes the beginning of a sentence can get choked
off--not getting enough air to be spoken at sufficient volume--when
someone first starts talking. Either that or the "I" and the beginning
of "wonder" get elided together. Basically (in either case) it's
probably a consequence of the tendency for most people to be lazy when
they speak.

I'm not a linguist but I've studied a bit of this stuff, and I've made
these statements without any actual research into the matter, so make
of it what you will.

Good luck,
smudgy.

Spoken language often uses verbal "shorthand." I see nothing wrong in
starting a sentence with "Wonder if...", unless the circumstances call
for the use of formal English.

To demand strict adherence to structural rules in colloquial speech or
in informal writing is, in words often attributed to Sir Winston
Churchill, "the type of arrant pedantry up with which I shall not
put."

I'm not sure I would want someone named Smudgy getting the laundry -
at least not if it was clean laundry!