The idea

Monarchical, dictatorial and oligarchic regimes are bad to live in because their policies often don't reflect the values of the people.  The ideal of democracies is to (somehow) ensure that governance happens in accord with their citizens' morality.

However, we have to keep in mind that while ethics can be set by majority vote, questions that can be settled by experiment are not subject to opinion polls.  And—perhaps unfortunately—not everyone is well-versed in everything from economics through medicine to urban planning.

The current implementation

Nowadays, most non-authoritarian countries use representative democracies for their government.  Thus every so often (commonly, every four years) the citizens get to vote, that is, choose who will represent them.  (In principle.  In practice, further difficulties e.g. gerrymandering can erode this.)

Now, even if we are somewhat generous to current democracies, and suppose that four parties have a chance to be elected, that's still only two bits of input.  Once every four years.  Thus the people have half a bit per year of control over their country, if they are lucky.  With a two-party system and manipulations, they have less than a quarter bits per year.

Separation of powers—what powers?

"Legislative, executive, judicial." Thank you very much.  In practice, though, there's very little difference (if any) between laws and "mere" decrees.  They both have to be complied with, or else.  As such, I think it would be better to give a more "detailed" list, more on the level of ministries within the executive branch:

Such a finer-grained separation of powers with no top-level integration would, at the very least, make it much more difficult for anyone to capture the state and turn it into some sort of semi-dictatorship.  But why did the current, easily-capturable structure come into being in the first place?

My answer is that most democracies were either created out of monarchies without completely dismantling the earlier system, or their creation was preceded by much discourse to this effect, or they were copied from other democracies.  That is to say, many monarchies went through a transition where the growing middle class couldn't dethrone the king, but the kings could be bargained into giving some power over to an elected prime minister, chancellor, etc.

And later, this arrangement could simply be extended by transferring increasingly more responsibilities to the PM, or—as in other countries—by eventually replacing the king with an elected head of state.  The title and the powers that go with it (a veto over laws passed by the legislature, notionally leadership of the armed forces, the paramount importance in diplomatic relationships and the power to sign treaties) clearly correspond to the powers of the king in a constitutional monarchy.

These were steps in the right direction.  However, it is common practice that the PM is elected by the same Parliament that is also the legislature, creating a situation where even the two traditional branches aren't separated, never mind a finer-grained division of power.  Even worse, in some cases even the "democratic king" is elected by that same Parliament.

How to separate them?

A first and obvious idea is to elect the PM and the head of state separately from the legislature.  This is one of the very few bits where I think the American political system does something right.

However, this only goes so far.  There cannot be dozens of elections, one for each position—and this would be a bad idea not only due to cost, but also because civil service requires knowledge and skills specific to the job.  Charisma and connections don't quite cut it.

Another point to keep in mind is that single-seat contests have a marked tendency to create two-party systems.  On the other hand, a group of 5 or 7 can both work very well, and can be elected in a way that allows multiple parties to work.  Single Transferable Vote and related systems (notably Schulze-STV) work very well for this purpose.

Wider input channels

If we want to get more information about the citizens' value system than half a bit per year, we need new ways to get that information.  And crucially, we must make such systems both binding on the government, and at least reasonably secure against tampering.  That's a tall order, I know.

Opinion polls
We already have the "technology" required to take representative samples.  With them, asking a few thousand people gives a pretty accurate picture about what the whole nation of several million think.
Focus groups
More in-depth and with more room for activity from below, focus groups can reveal false assumptions made by the "managers".  This is why companies are using focus groups to guide development of new products.
Citizen board
German public transit organizations have Fahrgastbeiraten, a body of 15-25 people who are asked every 3-6 months for input.  This is basically a permanent form of focus groups, or—if you want to look at it that way—something not entirely unlike a jury.