And she thanked members of the armed forces, many of whom will be deployed overseas at Christmas, for their efforts.
The Queen has had a memorable 2018, with two of her grandchildren – the Duke of Cambridge and Zara Tindall – welcoming new additions to their families.
Another grandson, Prince Harry, married Meghan Markle and they became the Duke and Duchess of Sussex, announcing soon afterwards that were expecting their first child, due in the spring.
Granddaughter Princess Eugenie wed long-term boyfriend Jack Brooksbank.
Bringing a touch of humour to her televised address, the Queen said: “Closer to home, it’s been a busy year for my family, with two weddings and two babies and another child expected soon.
“It helps to keep a grandmother well occupied.”
She also described the importance of having loved ones around her: “Through the many changes I have seen over the years, faith, family and friendship have been not only a constant for me but a source of personal comfort and reassurance.”
And she offered words of comfort for those missing relatives or friends: “At Christmas, we become keenly aware of loved ones who have died, whatever the circumstances.
“But, of course, we would not grieve if we did not love.”
The Queen also remembered her father, George VI, reflecting on his service with the Royal Navy during the First World War and the role he played in the early years of the Commonwealth.
Now aged 92, the Queen’s reign as monarch has lasted 66 years and she has been married to the Duke of Edinburgh for more than seven decades.
Sitting at a desk and with a Christmas tree in the background, she said: “Some cultures believe a long life brings wisdom. I’d like to think so.
“Perhaps part of that wisdom is to recognise some of life’s baffling paradoxes, such as the way human beings have a huge propensity for good, and yet a capacity for evil.
“Even the power of faith, which frequently inspires great generosity and self-sacrifice, can fall victim to tribalism.”
Footage of Harry and Meghan’s glittering wedding was featured in the broadcast alongside Eugenie and Jack’s nuptials, and also the moments when the couples kissed on the steps of St George’s Chapel at Windsor Castle.
The duke and duchess’s carriage ride was also screened.
The first of the two royal babies to arrive this year was Louis, and there was a clip of his proud parents, William and Kate, presenting him to the world outside the private Lindo Wing of St Mary’s Hospital, Paddington, where he was born on April 23.
And in June, Zara and husband Mike Tindall, a former England rugby player, welcomed their second child – a daughter called Lena.
“We have had other celebrations too, including the 70th birthday of the Prince of Wales,” said the Queen as the camera panned to a framed picture on her desk, an official image released to mark Charles’s milestone and featuring his wife, the Duchess of Cornwall, along with the Cambridges and their children, and the Sussexes.
The broadcast was recorded in Buckingham Palace’s White Drawing Room, surrounded by family photos.
They included William and Kate’s Christmas card image featuring themselves and their children, a picture from Eugenie’s wedding showing the bride and groom surrounded by their bridesmaids and pageboys, a black and white image from Harry and Meghan’s big day, and a picture of George VI.
The Queen hosted the Commonwealth Heads of Government Meeting in London in April and she noted that eight states attended the first such gathering in 1948 and were welcomed by her father.
She added that today the Commonwealth consists of 53 member countries with a combined population of 2.4 billion.
She said: “Its strength lies in the bonds of affection it promotes, and a common desire to live in a better, more peaceful world.
“Even with the most deeply held differences, treating the other person with respect and as a fellow human being is always a good first step towards greater understanding.”
As head of state, the Queen remains publicly neutral when it comes to political matters and does not express her views on issues.
But some commentators may interpret her words about respecting others who hold opposing views as a veiled reference to the toxic mood of the public debate around Britain leaving the EU.
The broadcast was recorded on December 12 before Prime Minister and Jeremy Corbyn’s angry Commons clash which, with Brexit at its root, saw the Labour leader accused of calling Theresa May a “stupid woman”, something he denied.
After footage was shown of a “thrilling” RAF fly-past, celebrating the air force’s centenary by forming the number “100”, the Queen aid: “We owe them and all our armed services our deepest gratitude.”
She also acknowledged the sacrifices of the thousands of seamen who died fighting in the First World War Battle of Jutland in 1916 during which her father served as a midshipman.
She said: “The British fleet lost 14 ships and 6,000 men in that engagement. My father wrote in a letter: ‘How and why we were not hit beats me’. Like others, he lost friends in the war.”
The Queen concluded her broadcast by highlighting Jesus’s message, often cited at this time of year: “I believe his message of peace on earth and goodwill to all is never out of date.
“It can be heeded by everyone; it’s needed as much as ever. A very happy Christmas to you all.”
With Parliament fundamentally divided over the way forward with Brexit and military conflicts still raging in parts of the world, the monarch’s words are likely to resonate with many.
The broadcast ended as it had begun, with singing from the choir of King’s College, Cambridge, famous, as the Queen said, for its Nine Lessons and Carols.
They opened the festive broadcast by singing the National Anthem and ended with the carol Once In Royal David’s City.