What you will not hear on headphones are phasing issues that are only apparent when the sound waves from two (stereo) sources interact and comb-filter each other. Although phones have two sound sources they are seperated by your head and the output from left and right don't interact and interfere with each other as they will in air.

"Monitoring" headphones aren't really intended for music mixing or mastering (speech and sound effects may be OK). They are useful so a singer or musician can hear what they need to sing/play along with at high quality and with minimal sound-spill that might be picked up by microphones. They are useful to listen to a soloed track sent to the phones bus while the main mix is still going out through monitors. They are useful while tracking as the engineer can use them to set up to record something while a conversation goes on around them in the control room.

They are invaluable for DJs or anyone else needing to set up the next song either in silence or without interrupting playback of the current song or who wants to hear what they are doing but also wants to block out most of the noise from the club system. Also for listening to a soloed mixer channel while mixing a live gig.

Closed-back headphones can also be very useful to find out what is going on in the bass if the monitors aren't capable of reproducing very low frequencies.

Headphones are very deceptive when used for mixing though, and can be tiring. It doesn't help that many tagged as "monitoring" phones are actually highly coloured if you look at their response curves. Marketing speak such as attaching "professional sounding" phrases to things plagues the hi-fi industry just as much as the many other inflated claims dreamed up by sales staff.

Finally, it is very easy indeed to go well into the danger zone of excessive noise exposure with headphones without even realising you are doing it.

One other use for headphones is to find out what your music will sound like on iPods, mp3 players etc., so it might be a good idea to add a set of genuine Apple earbuds and a set of cheap and nasty earbuds to your playback system.

There are also open backed headphones which for some reason have not been mentioned here so far.  These are usually much nicer sounding and have a flatter frequency response.  But they still suffer from the problems that headphones can create.
 
What may be interesting though is some of this software/hardware that replicates the sound of speakers in a room on headphones. But I have not heard or used such a thing yet so I am not in a position to comment on
that.  Perhaps someone that has and might have a lot of experience with that might be able to chime in.

TLW, that's awesome information I think...for me that's great to read.
Jeff, good suggestion too and I've tried such a plugin that emulates car speakers etc, but didn't know how to use it really.
For Tremo-Jem I have 2 more ideas maybe.
One is to just play back a few songs and try to get your monitors and audiophile set equally loud.
You could have 2 masterbusses then with sends maybe, and listen on 1 volume to both outputs and compare them.
One other thing I found handy is to load a reference song you know well, into your project and route it directly to the soundcard.
Then match the volume of the reference song to your project, you can A/B your mix quickly to your project with the solo button and then you get a good idea of 'where you are'.

I think the difference between headphone is dictated by the price and the brand.
 
I have £30 Sony Circumaural headphones, 16 Ohm. They are OK for playback on a media player. Previously I used Sennheiser Cx880i which were actually quite flat sounding. The bass needed a bit more gusto to drive it properly rather than a generic Creative Xen Player could deliver.
 
In my "studio" environment, I use AKG K702 Reference through a headphone amplifier or a Focusrite 2i4 depending on what I'm doing. Otherwise my portable reference would be a set of Shure SE425 in-ear monitors which whilst not the "bassiest" things are a good clean reference.
 
What speakers offer is that added ambience of your listening environment. Open Back headphones I find to be a bit more honest. My AKG K271 II headphones sounded great however never translated that well to speaker in my opinion although mids and highs were pretty reliable.
 
I'm wondering what will happen to the market in Apple's arena now that they have bought Dr.Dre Beats.
 
 

Thanks Wouter and others.
 
Another thing I would try is, play reference material on the Hi-Fi, A/Bing it against the mix I am sending to the system. If I get them even, then I should have confidence that I am not pushing my mix thru that system, any more than the powered studio monitors.
 
Cool...I think. An SPL is a great tool, but what I am trying to achieve here is not to be pushing an alternative system's level in an attempt to keep up with the studio system.
 
When mastering is complete...my goal is to have what I need in the mixing/mastering room so that I don't have to burn a CD and then go to those separate sources.
 
As a matter of fact I like the idea of adding a portable boom box (has to accept line in), a cheaper more common stereo set, a car radio set and a mono speaker "Auratone" as Jeff mentioned.
 
This way I can hear the mix/master on all of these sources without leaving the room or wasting CD material.
 
I like to check my mix as I am in the progress of working on it, at least once every three days as I go along, just to see where I am.
 
I am a newbie still...so thank for your help.
 
 

So I searched Radio Shack for the SPL Meter.
 
NOTHING
 
Back in the day I remember they had a nice one, but now I can't find anything.
 
Found them...geez, I checked meters, but is was under music and sound.

If you have an iPhone, there are some (but not all) apps that do fairly accurate measurements. I use one called NoiSee and my recollection was it tested within ~1dB of my Radio Shack meter. It was one of three (the cheapest!) tested apps that met US government occupational noise guidelines and costs $0.99. 
 
Unfortunately, other phones have inconsistent HW and sound capabilites, so apps can't be easily calibrated.

I check mixes on different sets of speakers but usually each set resides in its environment. 
 
I do have a couple of alternate pairs in the studio but I don't really use them that much anymore - sometimes I do try the little Alesis M1.
 
A couple of years ago, my wife bought this cube/dock station (mono) for the gym. That thing is nowhere near hifi. But that's usually my first stop to check a mix, and since I listen to music on that thing every day while working out, it gives me a good idea of what works and what doesn't.
 
Usually I'll listen once in the gym (where the cube is) and then go to the adjacent room and listen from there, "casually" so to speak...
 
I know some people think it's heresy but I also check my mixes on the Macbook's own speakers. This needs to be put into perspective - I wouldn't make a decision based on that, but it sometimes gives me an indication of how my mix translates compared to a commercial release.
 
Then there's the car. 
 
I believe that anything you're used to can provide you with a bit of insight, even though you need to establish a hierarchy.

Rain
I know some people think it's heresy but I also check my mixes on the Macbook's own speakers.

 
I cringe every time my kids and their friends play music through their laptop speakers.
 
It seems that as long as the music is recognizable, the brain can do the rest.
 

Paul P

Rain
I know some people think it's heresy but I also check my mixes on the Macbook's own speakers.

 
I cringe every time my kids and their friends play music through their laptop speakers.
 
It seems that as long as the music is recognizable, the brain can do the rest.
 

So do I - and my wife does play music on hers all the time. But when I started writing for her, I realized that I should maybe take that into account. After a while, you develop a certain frame of reference. Good mixes sound a certain way. Bad mix sound even crappier than the rest.