Right now?
little.
The current opressive power of nations as per 2018, even the smallest one, is times bigger than any other nation in the past, for the simple reason that weapons, armament, and technology is what wins wars today.
The biggest civilian armed resistance moment we're seeing in our times are both the Syrian opposition coalition, and the Kurdish freedom forces.
The syrian opposition coalition survived as long as material resources and diplomatical restraint from the Assad goverment forced the combat operations to be developed in 20th century fashion, columns of dozens of vehicles approach site X; a small artillery attack with light/medium equipment barriages the military hotspots, and infantry clears the streets.
This is the only case where a civilian armed force could win, guerrilla urban warfare.
What we're seeing now since Russia, Usa and Turkey's intervention these last years due to Daesh and economical interests are grand strategy battle plans, with multiple bombardments, strategical attacks, use of non-regulated (chemical, etc) weapons, and mass artillery that drive the infantry attacks unnecessary and the rebels almost completely defenseless.
When does it work? when facing a similar equipped, armoured and trained force like the Daesh vs Kurdish forces conflict, where the kurdish resiliance turned the tables even when being attack by both sides of the conflict, or the "civil war" going on in Ukraine, where the "rebels" have access to similar military equipment.
In the near past?
We have dozens of examples of 20th century conflicts where a civilian armed force ( depending on the side of the media, "terrorists/rebels" or "freedom fighters/patriots") have managed to drive back the push of a much stronger military force, for a short time.
In the end, a stronger military force will always succeed, unless the political leadership behind it starts to weaken. The Irish revolts, Vietnam (and the previous forgotten chapter of the French indochina war), the Soviet–Afghan War are examples of wars where it just wasn't worth it for some very big players to keep up the fight.
in the far past?
The greatest examples come from the early 19th and 18th century, the Peninsular War in Spain (1808-1812) started with the conservative and anti-french religious figures ( mostly church lawyers and priests ) stepping up and arming with their money and assets ( and brittish and portuguese help) the civilians,some episodes of the french revolution ( althought most of it was urban-ish), the American revolutionary war, and the always forgotten tragic ending of the Spanish Succession War, where 10000 militiamen and ex austrian-aligned military members (about 50% of each) stayed under siege for 380 days in barcelona defending against a force of 32-50.000 men ( depending on the stage), plus a full fleet port blockade, and them( defenders) winning every assault intent during the siege except the last ( where only 4000 defenders were left).
In the very, very far past?
During the renaissance and the medieval ages, armed civilians ( and specifically, those veterans in conflicts) were a constant headache to feudal nobles, causing commoner wars, rebellions, religious insurgences... due to them being the core of an almost pure "on-demand" recruitment system with no standing armies.
conclusion
A ruthless, not politically restrained, well trained and equipped modern ( 2018) standing army ( and navy + air force) will always win an armed conflict against civilians.
Change any of the parameters and the odds will turn into the civilian's favour a little bit.