I recently came across bitcoin, it is what I was really looking for at the time.
money.stackexchange.com/users/1965/triforcelink
You say you want a more "stable" system.
Recall from your introductory economics courses that money has three roles: a medium of exchange
(here is $, give me goods), a unit of account (you owe me $; the business made $ last year), and a store of value (I have saved $ for the future!).
I assume that you are mostly concerned with the store-of-value role being eroded due to inflation.
But first consider that most people still want regular currency, so as a medium of exchange or accounting unit anything would face an uphill battle.
If you discard that role for your currency, and only want to store value with it, you could just buy equities and commodities and baskets of currencies and debt in a brokerage account (possibly using mutual funds) to store your value.
Trillions of dollars' worth of business takes place this way every year already.
Virtual currency was a bit of a dot-com bubble thing.
The systems which didn't go completely bust and are still around have been beset by money-laundering, and otherwise remain largely an ignored niche.
An online fiat currency has the same basic problem that another currency has.
You need to trust the central bank not to create more money and cause inflation (or even just abscond with the funds... or go bankrupt / get sued).
Perhaps the Federal Reserve may be jerking us around on that front right now....
they're still a lot more believable than a small private institution.
Some banks might possibly be trustworthy enough to launch a currency, but it's hard to see why they'd bother (it can't be a big profit center, because people aren't willing to pay too much to just use money.)
And an online currency that's backed by commodities (e.g. gold) is going to be subject to potentially violent swings in the prices of commodities.
Imagine getting a loan out for your house, denominated in terms of e-gold, and then the price of gold triples.
Ouch?
money.stackexchange.com/users/None/
Congratulations!
You see the problem.
You can't get away from unstable currencies.
The other problem is that the US will shut down anything that appears to be providing a replacement for the US Dollar.
Once a token or medallion or gift certificate or whatever starts being used outside the confines of one business or one network of businesses, it will be shut down, quickly.
It happened with Las Vegas gambling tokens .
Another more recent attempt was with the Liberty Dollar , gold and silver coins and certificates that not only had precious metal backing, but whose proponents encouraged taking them to retailers and paying with them as if they were US Dollars.
There were other problems with this idea, but it was the competitive stature of the Liberty dollar that got the headquarters raided and the main site shut down .
Basically, all signs point toward dealing with currencies and their state of being systematically eroded over time.
If you do find one that appears to exist, be wary, because the rules can change at any time, and the "money" will be nowhere near as liquid as a proper currency.
money.stackexchange.com/users/414/mbhunter
Edit: I discovered Bitcoin a few months after I posted this answer.
I would strongly recommend anyone interested in this question to review it, particularly the myths page that dispels much of the FUD.
Original answer:
Although it is not online, as a concept the Totnes Pound may be of interest to you.
I live quite close to this village (in the UK) and the system it promotes does work well.
According to the Transition Town Totnes website this means that it is "a community in a process of imagining and creating a future that addresses the twin challenges of diminishing oil and gas supplies and climate change , and creates the kind of community that we would all want to be part of."
If you are looking for a starting place to introduce a new type of currency, perhaps in response to over-dependence on oil and global trade, then reading about the Transition Towns initiative could provide you with the answers you're looking for.
money.stackexchange.com/users/2009/Gary Rowe
I'm the equivalent of the FED at ROBLOX.
I run a virtual economy there worth millions of dollars.
Even though we are in the business of printing our own money, we've seen much more stability in our currency than in the USD.
It actually appreciates over time.
I don't think it would make a good investment though, nor would any of the online virtual currencies that I am aware of.
money.stackexchange.com/users/1949/John Shedletsky
I'm not sure, but I think the monetary system of Second Life or World of Warcraft would correspond to what you are looking for.
I don't think they are independent of the dollar though, since acquiring liquidity in those games can be done through exchange for real dollars.
But there can be more closed systems, maybe Sim type games where this is not the case.
I hope this helps.
money.stackexchange.com/users/1930/Raskolnikov
This site lets people deposit gold into an account.
Once you have an account setup you can pay others in gold online .
I haven't used it or know of anyone who has so
I cannot provide any feedback to how well it works.
money.stackexchange.com/users/1229/Muro
I'm actually looking for something that would resemble a monetary system of a sovereign country. The value of its currency would be somewhat independent of, say the dollar. If there was a more stable system online, maybe it could replace the less stable real world systems.  I'm just curious if anyone has heard of anything like this, or if there is place i can read more about related topics.
Do you know of any online monetary systems?
money.stackexchange.com
<currency><online-payment>
money.stackexchange.com/questions/4572
money.stackexchange.com/users/1965/triforcelink
Bitcoin would be similar to this concept. You could also look at local currency like the Totnes pound or video game currency like Second Life. Two examples of online currency include Bitcoin and the Totnes Pound. Currency systems used in games like Second Life or World of Warcraft may also fit this description.
Two examples of online currency include Bitcoin and the Totnes Pound. Currency systems used in games like Second Life or World of Warcraft might fit this description.