Headphones
More often than not, the proprietary headphones that manufacturers supply are in the box are dire, so you'll probably want to use your own headphones. Look for a 3.5mm jack so that you can plug in your own ear pieces, or else suffer the indignity and discomfort of rubbish headphones.
Storage
Next most important in the music-phone palyer stakes is media storage. If you want to take your music with you then you're going to need somewhere to put all you tunes. With any media device, the larger the memory the better simply because it allows you to hold more of your favourite music. If the internal memory on the phone isn't up to much, at least make sure the phone's memory can be expanded via SD card. An SD Card is a very simple way to bolster a devices memory.
Both models in Nokia's X6 range comes complete with considerable on-board memory banks - the Nokia X6 32GB and the diet, Nokia X6 16GB Edition, while the following allow expasnion of up to 32GB: HTC Desire, HTC Legend, Sony Xperia X10 range, Samsung Galaxy S, Samsung Wave, the LG GD880 Mini, the list goes on.
Controls
Next most important in choosing a music phone, are controls. Some mobile phone manufacturers include a set of dedicated controls, which save you the bother of getting your phone out of your pocket each time you want to cycle trough tracks or turn up the volume.
Nokia have included dedicated controls on its range of XpressMusic phones - from the compact Nokia X3, to the 5630, 5132, 5310, 5730, 5235, 5130, 5530, 5800. Meanwhile the Blackberry Curve 8520 is RIM's first phone to have dedicated music player buttons and has proved very popular with the always-connected / youthful music-loving segment.
Audio Quality
Most devices have some sort of MP3 player these days, however if you're an audiophile who only wants the finest quality sounds, then you will want to make sure that the media player supports loss-less and un-compressed file formats such as WAV/AAC/ FLAC.Look for these in the phone's spec sheet under "Media Player".
Sony Ericsson have a range of walkmen phones that boast the FLAC format - The Sony Ericsson Zylo and the Sony Ericsson Spiro.
Streaming
For those of you who prefer to use streaming music services then you should look for maximum connectivity. Some like Spotify do allow you to make your playlists availabel offline, but you'll still need a decent connection to backup them up to your phone in the first place. Look for WiFi and the best 3G connection you can get, ideally HSDPA-enabled 3G.
Be aware however, that streaming over the netork is an extremely data-hungry exercise, so ensure that you have a decent data plan in place, or you'll end up with a very large bill. Further to that point - if you are abroad STREAM AT YOUR PERIL, data prices when roaming are nothing short of deadly and unless you don't mind paying off a sky-high phone bill, you'll turn those services off before you take off for another country.