This is just copy pasted from bruhaha from yahoo answers, clearly the most reputable source (and seriously the first google search result):

(Much of this is a rewrite of a recent answer I gave for “smile”, which runs into similar problems. I’ve tried to make it a little clearer. It IS a bit long, but please bear with me and I think it will make sense.) 

I find it odd that some say they have checked several dictionaries, including dictionary.com – and they all have only ONE syllable. 

Sorry, but the first entry for “hour” at dictionary.com provides two alternatives – one with one syllable, one with two. 

So your question is quite a good one. You’ve actually stumbled on a problem with syllable-division that affects one whole cluster of words in Modern English – specifically words in which the “long i” OR the “ou” sound (written “ou” or “ow”) come before the L or (especially) R sounds. 

I’ll try to explain why this problem exists, and how it tends to push us to turn things that supposedly should have one syllable into something that at least SEEMS to have two syllables. 

1) Part of the reason for the problem is that both of the vowel sounds are “diphthongs”, that is two vowel sounds combined into one. Note that our “long i” vowel, even though often written with just one letter is, in fact the combination of two SOUNDS – “ah” and “ee” ; “ou” is (more obviously) “ah + oo” (the u sound). 

2) Now notice the English “semi-vowel” sounds, most often represented by Y and W. Y at the beginning of a syllable makes the consonantal y- sound (as in “yell”); elsewhere it makes an e/i vowel sound (as in “my” and “any”). W at the beginning of a syllable is consonantal “w-” (as in “well”); after a vowel it makes a u-vowel sound (as in “cow”, “law”, “few”). 

3) Finally, when you try to pronounce those long-i and ou diphthongs before an R or L it is difficult (mainly because you have to shift your mouth position so much) to smoothly pronounce the whole things as one syllable.

What happens is that the final parts of the diphthongs (the “ee” and “oo”), which we just saw are forms of the Y and W “semi-vowels” tend to shift to CONSONANTAL pronunciations AND to insert a short unaccented vowel (called the “schwa” sound) before the R or L, to make it all easier to pronounce. 

For quick comparison: it’s easy to say “might” as one syllable, but “mire” is harder; similarly with “out” and “(h)our”. The latter tends to become almost “ower" 

______________ 

Compare these four sets of words: 

* our/ hour – may sound the same as power, shower, tower, though you can see from the SPELLING that the second group was understood as two-syllable words, the second syllable beginning with the consonantal W sound, 

i* re/hire/tire… – "one syllable”, yet do we really pronounce “hire” so differently from the two-syllable word “higher”? 

This is all much more pronounced with R, but it happens to some extent with L as well. 

* owl, cowl, scowl, foul – ‘one syllable’. But compare “towel” – one syllable or two? 

* mile, smile, tile, aisle… OK, now… do we really clearly pronounce these as having ONE syllable, as we do with this vowel in words like mine or rite? Can’t you hear at least a HINT of the consonantal “y-” sound and a very slight unaccented “uh” before the L ? 

No, “fire” is not quite as clearly two distinct syllables as “fighter” is… but it also isn’t as simply one syllable as “fight” is. The truth is, this whole set of words is 'on the edge’, not simple one-syllable words, nor quite clearly two-syllable. It all depends on how you decide to understand that little extra vowel sound… or how distinct it happens to be in your own speech. 

Dictionaries vary on how they indicate all this, but sometimes you will see indications of this problem, e.g., in the listing of TWO pronunciations for words.

Observation to those who insist that it MUST be either one or two. The very IDEA of “syllables” is actually an attempt to DESCRIBE what we actually DO when we speak. Spoken language itself is the most important thing, not the terms and “rules” we use, and sometimes impose on language, to try to explain it (and, we hope, make it easier to use well). 

We should not be surprised that our nice, neat terms, rules, etc., don’t always perfectly fit every case (and they don’t need to for them to be useful). It is not a cop-out to suggest, then, to suggest that a word like “hour” might be described as 'somewhere between’ one and two syllables, and perhaps varying according to where it is used by whom (dialect).

What’s your take on this?