Mr Cameron hailed the shared history of Scotland and the other nations of the UK building the industrial revolution, fighting two World Wars, creating the NHS and staging the Olympics.
And he dismissed Scottish National Party leader Alex Salmond as a "man without a plan" whose proposals for an independent Scotland were "all over the place".
He told delegates at the Conservative Spring Forum in London: "These four nations. Three colours on the flag. One incomparable United Kingdom.
"We love this country and all it stands for - so let's win this referendum for all our futures.
"Our next big fight: the one to keep our United Kingdom united.
"Let us set out our positive vision for the future of the UK."
Setting out his case for the UK to remain united, the PM asked: "When the future belongs to the innovators, why would we want to put up walls between the bio-engineers in Edinburgh and Cambridge?
"When stability and certainty are what brings in investment, why would we break apart one of the oldest and most successful single markets and currencies on the planet?"
But he said that supporters of the union were fighting for a No vote on September 18 "not just because the UK works - which of course it does - but because we love this country".
Scotland and the rest of the UK have "ties that run rich and deep", said the PM.
"Two hundred years ago we were leading the industrial revolution and shaping the world's economic ideas.
"One hundred years ago young men from the Highlands to the Valleys went to war together, and many fell, together.
"Seventy years ago - the D Day landings, the Highlanders running onto the beaches of Northern France to the skirl of the bagpipes.
"Sixty years ago - building the health service that says no matter where you're from or how much you've got, we will look after you.
"And one year ago - the single-tier pension, which says if you've worked hard all your life we will support you - a mark of respect for those who have worked hard all their lives and a symbol of our solidarity on these islands."
Mr Cameron rejected the argument that flying the flag is wrong and taking pride in Britain's history "vulgar".
"I say no," he said. "Head for head we are a people that has influenced and improved the world like no other - and this is what I'll proudly teach my children."
He cited the UK's democracy and its celebration of injured war veterans in the Olympic torch parade as examples of what made him proud.
"This is what I love about our UK," said Mr Cameron. "The decency. The family. The solidarity.
"The health service we built together, the help in hard times we provide together, the starving people around the world that we help feed together, the freedom we fought for together."
Mr Salmond's desire to have independence while keeping the pound was "like someone asking for a divorce and then saying 'but do you mind if I keep the joint bank account and credit card?'," said Mr Cameron.
And he added: "Alex Salmond talks about having a plan for Scotland... yes - he's on draft 83.
"The reality is, he is a man without a plan - and let's be bold in saying it."
Scotland's Deputy First Minister Nicola Sturgeon said: "If the Prime Minister really felt secure in his arguments, he would come to Scotland and debate them with the First Minister and the people of Scotland - instead, he delivers yet another lecture from London.
"Mr Cameron talks about the importance of the health service as he steadily dismantles it south of the border, and he talks about providing help in hard times - as his Government's welfare cuts force more and more people in the UK to turn to food banks.
"It is only because Scotland is already effectively independent in terms of health policy that we still have an NHS worthy of the name in Scotland, and we need to control welfare policy too by voting Yes.
"Only independence can allow us to use Scotland's vast wealth to build a fairer and more prosperous country - that's why poll after poll shows the Yes vote increasing, while support for the No campaign has stalled.
"The real problem for Mr Cameron is that, after one of his senior ministers was last week caught telling the truth on currency, no one believes a word that the anti-independence campaign says any more."