How do you listen to more than one portable audio device
simultaneously, using headphones? Do you need some kind of mixer?
Obviously the solution needs to be portable and preferably support
more than two devices.

To use a single microphone with audio inputs, all you need is a
splitter, but I tried a splitter to mix two mp3 players' outputs, and
one of the mp3 players started having errors that I suppose were due
to unexpected voltage (I'm no electronics technician...)

Why?
I want to listen to
1. my mp3 player
2. my telephone
3. my pda
...and not remove my headphones.

Yes, you need a mixer.

      Combining outputs of the electronics devices DIRECTLY 
      may lead to all kinds of trouble, including fire or blown fuses.
      Audio output assumes certain passive impedance, not another voltage source.

You also need to control all those devices and selecting
which mix (contributions of diffrent sources) you want to hear,

So, I would recommend as a solution a combination: 


1) Bluetooth Headphones
2) a computer with blue tooth 

  2)  could be a laptop or tower, which can play MP3, pick-up phone ...
      host mixer software and interface with other devices.
 Some devices,
      (e.g. mobile phones come with blue tooth ) can talk to headphones
 directly, others can be interfaced to computer by other interfaces
and mixed in software, then computer will transmit their signal to the
headphones.

re 1)
http://www.electronicsoutfitter.com/store/et2000.html
http://amos.shop.com/amos/cc/main/ccn_search/st/'bluetooth'+headphone/sy/productsx/ccsyn/260/prd/18516296/ccsid/409806748-27283/adtg/06030523
http://www.cambridgesoundworks.com/store/category.cgi?item=l1cb253b&adcode=WFROOGLEB3
etc

re 2)
So What is Bluetooth?


Bluetooth is a very simple type of wireless networking that can allow
up to eight devices to be connected together in a mini-network.

 Here is non-technical explanation of the blue-tooth networking



http://www.thetravelinsider.info/roadwarriorcontent/bluetooth.htm

http://www.cambridgesoundworks.com/store/category.cgi?item=l1cb253b&adcode=WFROOGLEB3


You may use a 'blue-thooth router' as a hub 
http://shopping.yahoo.com/s:Router:3037-Wireless=Yes:4050-Networking
Standards=Bluetooth

but I recommend to use a computer, a laptop nearby, as a controler/recorder


here are some screenshots, which shows how software mixer looks
http://www.lynxstudio.com/manuals/LynxTWOMixerAddendumMac.pdf

 these are from Mac, but all systems, MS windows, linuc, Mac have these included. 

This is a hrdware mixer 
http://www.tweakheadz.com/choosing_a_mixer_for_your_studio.html
and these cost $100 - $200 (more for prefessional music mixers)
http://www.bizrate.com/buy/products__att278369--271017-,cat_id--521904,keyword--Dj
Software.html

but software emulations is less expensive and ultimately more flexible.

If mixers which come free with computer OS are not enough, you may buy
costom software which allows different modes of mixing

http://www.audioutilities.com/mp3-dj-mixer/mp3-dj-mixer.htm

Hedgie