If bitcoin ever goes mainstream it will surely ruin the lifes of all the ones invested in fiat (see
https://bitcointalksearch.org/topic/bitcoins-dystopian-future-180798). Gresham's Law will destroy their fiat savings, since everyone will want the stronger bitcoin and will dump fiat, devaluating it. We'll see it happen first in the troubled economies, with high inflation and generalized suspicion on governmental money because of past problems.
And I have little doubt that bitcoin won't bring any equality, on the contrary. It will make us bitcoiners rich, but it will be at the expenses of fiat holders.
Because I doubt bitcoin will bring much prosperity, since it will establish a deflationary monetary system. But maybe it will be possible to minimize those deflationary effects:
a) Commercial banks will adopt a bitcoin fractional reserve system, lending bitcoins with only partial support on their holdings. That will allow an artificial (banking) expansion of the amount of bitcoins, thanks to the so-called banking money multiplier.
But since it will be hard to keep a trustworthy insurance of deposits (the government won't have enough bitcoins for that and can't create them), the system will be much more susceptible to runs.
And the interest will have to be high, because most people will prefer to have the bitcoins in their own wallets. So, forget about low interest rates. Well, high real interest rates (aggravated by potential deflation) can ruin any economy, since they thwart many productive investment based on credit.
b) It also might be created a bitcoin pattern, with governments printing money freely convertible in bitcoins. But I can see already the runs on the government on times of crises.
How will the central bank in depressions stimulate the economy?
It won't be possible to do any quantitative easing. Borrowing bitcoins to lend them at cheaper interest rates to the commercial banks won't be cheap.
How will the Government control massive tax evasion, especially if the anonymity of bitcoin improves?
They will find a way, nothing has destroyed the State in more than 13 thousand years of hierarchical societies. Bitcoin won't be able to do it. It seems we will be subject to intense control of our use of the Internet in order to track our earnings and spending of bitcoins. Some we'll be able to evade it. But the majority won't.
Will the volatility of bitcoin ever end?
The increase of its users will keep bitcoin's price going up. However, because supply and demand is controlled by human perceptions and emotions, after a huge boom in price it will always come a bust. Every overshooting of the price will be followed by a general perception that the price increased too fast and, consequently, by a drop.
For volatility to end, it would be necessary a general adoption of bitcoin that would limit in percentual terms further increases of new users taking in account the already large numbers of users. Currently, since the number of users is relatively low, it's easy to see its numbers increase for more than 30% in a short period. But since the numbers of bitcoin are limited (and the current rate of increase is relatively small and it will be again limited in 2016), the ending of volatility would also require or a stagnant GDP or a fractional reserve system based on bitcoin that would allow its banking numbers to artificially increase side by side with GDP. That won't happen for years. Volatility is here to stay for long.
Will this scenario be the future?
It's impossible to say. But bitcoin seems to have already a too strong standing to fade away on it own.
Another better alt coin might be a stronger obstacle than fiat. But bitcoin can always adopt any improvements.
Can governments still destroy it?
An international coordinated effort against the main exchanges and sites could indeed hurt heavily bitcoin. Even our own wallets are susceptible to attacks by virus/worms (remember Stuxnet?) and the network can also be affected. Access to it can be blocked by ISPs at governmental command. Many could evade these blocks, but the major part of the bitcoiners would give up, taking in account also the risk of sanctions. That indeed would spook major investors.
This can still happen and it will happen on troubled economies. The outcome is anyone's guess, it would depend on governmental coordination and level of effort. Governments lost similar wars (drugs, alcohol, prostitution), but bitcoin is an easier target than these activities. It's not a surprise that, besides scams, governmental repression has been the main negative driver of price.
What would be the consequences of this massive adoption over the price?
I can't even imagine what would be the price of bitcoin. Forget about all the low previsions you read before.
But the genie is out of the bottle. There is nothing we can do, except tell about it.
added 14 March 2015:
What is bitcoin going mainstream?
One can use different criteria.
1) A percentage of the amount of the total expenses on one year. But even 1% would be huge and would imply a very high price for bitcoin. However, according to the mentioned Gresham's Law, bitcoin will be hoarded and only rarely spent. It's like gold. Gold is part of mainstream, but people don't exchange it much, they prefer to keep it. On the main functions of money, mean of exchange, unit of account and reserve of value, I think the last will be bitcoin's main function. It won't be used much as unite of value, because of its volatility (many places that accept bitcoin prefer to announce the prices in USDs). It won't be used a lot as mean of payment, because people will mostly hoard it.
2) Accessibility: the fact that anyone can easily buy, sell and pay with bitcoin. Clearly, this is decisive. If we could exchange and spend bitcoins on the majority of banks' ATMs and retailers, we could say bitcoin is mainstream. But imagine that even in these conditions bitcoin kept being scarcely used, with small demand. It wouldn't be mainstream. Many physical businesses complain they never had customers paying with bitcoin. So, this is a necessary condition, but it isn't enough.
3) A percentage of people owning it. This seems to be a good criterion. But it isn't easy to establish a number: 10% seems enough, but not 1% or even 5%. 70 or even 350 million users on the all world would be great, but not enough for talking about mainstream. I guess only at 10% we would start to see unfold the problems above mentioned. But this kind of projections is hard to make.
Think about Paypal (I hate it, but let's use it as example). Is Paypal mainstream? I don't think so. It had a volume of transactions of only 180 billion on 2013, about 150 million active registered accounts and in many countries you can use it as mean of payment only on a few places. So, it reached about 2% of world population.
Bitcoin had about 23 billion USDs in trade volume alone during the last 12 months (see
http://www.bitcoinity.org/markets/list?currency=ALL&span=6m, at current price) and maybe 1 or 2 million active users. It still has a long way to go.