They're called iPods. It's become sort of a generic term for the digital music player. Even the term 'MP3 Player' isn't entirely accurate since MP3 is not the only portable music file format out there. Digital music players originally appeared in the form of Sony's Minidisc, then later portable CD players with MP3 capability. Then came the iPod and everything changed. Unlike the portable CD player, it was smaller and could hold a lot more music. The original could hold up to 20gb of music, compared to MP3 CDs which could only hold 700mb and the Minidisc which could only hold 1gb max.

The iPod itself was one of the first true MP3 players. It has become an iconic symbol of this generation. Apple has three iPod models currently in production. The iPod (aka iPod Video), the Nano, and the Shuffle. The Shuffle holds 1gb of music and costs $79 US. The Nano ranges from 2gb-8gb and starts at $149 US. The full iPod has either a 30gb or 80gb drive and starts at $249 US. The Shuffle and Nano use flash memory while the iPod uses a mechanical hard drive.
While the iPod is one of the most common MP3 players out there, it's not the best. They're expensive, particularly the Nano which seems cheap at $79 but lacks a display and FM radio. In terms of playback, formats are limited. The iPod can only playback MP3, MP4 AAC, Apple Lossless, AIFF, and Wave. The iPod features an interesting form of DRM as well. You can upload songs to your iPod but you cannot download them back onto your computer, which is pretty stupid. Even DRM king Sony allows two way transfers. Audio playback is good but throw away the crappy earbuds that come with it and get decent ones.
Positive points includes video playback with the iPod (Video). It's robust HDD, up to 80gb can hold a lot of movies which you can buy from iTunes or rip and convert yourself. It can playback most current video formats at a resolution of 320x240. The iPod wins out in terms of storage space. It's ideal for those who have large music collections. The flash based players are not worth it though since there are cheaper players which are just as good but offer more robust features.

If anybody were to create an iPod killer, it's Creative Labs. The makers of the well known Soundblaster series of PC soundcards. The Zen players come in a wide variety of shapes and sizes. I own the Zen Nano Plus. It's about the size of a pack of gum, gets long playback on AAA batteries, and has features such as a backlit display and FM radio. Excellent sound quality, it supports WMA and MP3 but that's it. That's the major drawback. The Zen Stone Plus has phased it out. Similar to the iPod Shuffle, it has 2gb or storage and a built in rechargable battery. Supports WMA, MP3, Audible, and Wave formats. Also has FM radio and a display.
In competition with the iPod Nano is the Zen V Plus. Similar in features to the other players, it has an OLED screen that can display photos, like the Nano. However, it can store up to 16gb on its flash drive. Unlike the Nano, it's cheaper. Starting at $80 for the 2gb. Same features, same quality but for less. Sounds like a good deal to me.
Next in line is the Zen Vision W and Zen Vision M. The M is similar to the full iPod. It comes with either a 30gb or 60gb mechanical HDD. It supports the same audio formats as the above players but it supports a much wider array of common video formats than the iPod does. Additional formats include DivX, Xvid, and WMV. Video resolution is the same as the iPod.
The Zen Vision W takes things a step further by adding 480x272 res widescreen video. It's identical to the M in every other way
Finally the vanilla Zen Vision. It has the same features as the other two, except for one. A 640x480 res screen. That's 480p DVD quality video on the go. One downside with this player is that it only includes a 30gb HDD. Still enough for several full length, uncompressed movies. The Zen Vision M starts at $249. Same as the iPod.

Sony is next on the block. They do make some portable audio players under the Wakman line. None worth looking at. If you're considering a Sony MP3 player, the Playstation Portable is the only way to go. Good audio playback, it supports MP3, WMA, Wave, and MP4 AAC. It's also capable of streaming audio wirelessly which the above players cannot. You can use either the "Location Free" media server or several of the free server tools that exploit the audio RSS features. Video playback is good with all popular formats supported. Video is widescreen at 480x272 resolution. You can also buy feature length movies on Sony's proprietary UMD discs. The downside with the PSP is that it's limited to 8gb of storage using Memory Stick Duo cards. This is highly limiting for such a device. It also skimps on maximum volume and lacks a manual equalizer. The PSP does not force the use of any DRM oddly enough though it can playback DRM content if necessary. Unlike the others, the PSP plays games as well with near Playstation 2 quality graphics. It can also surf the internet. Despite it's lack of storage, it's robust features make it a good deal. The core system costs around $180 US. Larger memory cards cost extra. A 4gb card can be found for about $80.

Lastly for today, we'll look at the Microsoft Zune. Designed to be an iPod killer, the Zune is an absolute joke of an MP3 player. The Zune sports an 30gb mechanical HDD with a 60gb model on the way. Also included is video playback at 320x240, FM radio, and Wifi. The Zune supports MP3, WMA, and MP4 AAC for audio. However, only WMV is supported for video playback. It is an uncommon format where MPEG and its derivatives dominate. The Zune has Wifi but can only communicate with other Zunes, making it useless in the real world.
The Zune uses a highly intrusive DRM method. It actually implants a virus into music files that limits the number of times a song can be played or shared when using Wifi. No other player looked at uses this kind of DRM methods. In fact, most didn't use DRM at all, even Sony's. The Zune also cannot playback songs legally purchased from many places such as iTunes, Napster, Yahoo, and even MSN Music Service. It does not comply with Microsoft's own "Play for Sure" coding that these sites use. WMA with DRM is being force on users. It's better to just use MP3.
The Zune is perhaps the worst product Microsoft has ever created and probably the worst MP3 player on the market. The device costs $250 for 30gb but is far inferior to the Zen Vision M and iPod that both sell at the same price point.