Most background bio sharing takes place in game, usually in the form of a conversation about a particular character's past. Occasionally, they will put up something online in the form of a short story or somesuch, but rarely
well, my In Game Bio is little more than ((RolePlayer)) and a breif description beyond what the game shows (accent, or visable things that arent...actualy visable IG) mainly because of the tendancy of n00b RPers reading bio's and using things in there even though theres no reason they would know (same as how they instantly know your name or that your a 'hero' or 'villain')
A brief security file can be found here (although anyone reading it should remember that information on there would only be OOC knowledge unless they have access to longbow, or EVIL's records)
and theres also (since Lunk has been around since just after US release, and i like to be thorough) a steadily growing 20KB text file, containing backstory, family history, tech spec, criminal record, time line back to 1932, and various tidbits.
.... but your no one is getting their hands on that.
I think maybe I have too much Bio 
There's certainly no shortage of creative juices amongst CoX players, as a quick scan of the Creative forum shows! 
Sometimes people will post their bios on the forums, but generally if people are inclined to post then they tend to expand them into full stories. The important thing is that people want to share their creativity. If you're proud of your bios then share them!
It's also worth remembering that if you're into RP, then many RP Superroups have their own forums where members post stories, bios, and other works to share and to help expand on the character they play. Our RP Supergroup, The Militia, does exactly that and I like to think that we have quite a thriving creativity community! 
Formerly @Crimson Archer, now @CA
The Militia - Protecting Paragon City through roleplaying since June 2006!
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Sometimes people will post their bios on the forums, but generally if people are inclined to post then they tend to expand them into full stories. The important thing is that people want to share their creativity. If you're proud of your bios then share them!
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I have had quick look through creative forum....but not quite sure I'm ready for that level of publicity yet :P
but thanks for the tip! Also had a look at your SG site, looks like you guys have a lot of fun!
What should one do if looking to find a way into said lively community?.... 
If you mean The Militia forum community, then just register on our forum and introduce yourself!
It is mostly for Militia members, but if you're interested in joining The Militia too, then we can discuss that. Just remember that we are a Roleplaying Supergroup. 
Formerly @Crimson Archer, now @CA
The Militia - Protecting Paragon City through roleplaying since June 2006!
If you wish to share biographical and "news" items then please consider Cery Industries - the only downside of this services is that its hero only.
So just completed writing all bios for my 4 characters and feeling pleased, but where can I view other people's bios.
I know about the right-click info when you meet people in game, but is there any other medium where people can share their back stories. I am keen to know what other creative juices have created elsewhere in ppls minds!