Both have provided hours of entertainment for children across the world.
One is the simplest toy, the other a fiendish puzzle.
Alongside the Barbie doll, Lego bricks and the Rubik's Cube are among the best toys of all time, according to Hamleys.
The toy store made a 'hero' list with the help of industry buyers to mark its 265th birthday and included toys that had cultural impact, enduring popularity and historical significance.
It said Lego - released in 1958 - is 'timeless, creative, and a global phenomenon', noting it has inspired films and theme parks.
More than 500 million Rubik's Cubes have been sold since 1974, making it the world's best-selling puzzle toy.
And it said more than one billion Barbie dolls had been sold since its release in 1959, making it a 'pop culture icon' across the decades.
Monopoly, the Tamagotchi virtual pet, the Nintendo Game Boy and the Furby also made the list.
Hamleys added that 'eternal classics' such as the hula hoop, spinning tops and marbles are still bought today, despite them being among the first toys sold when William Hamley opened the store doors in 1760.
Victoria Kay, head buyer at Hamleys, said: 'Once you start looking at this, it turns rapidly into a nostalgia-fest - even for toys from four or five years ago.
'My personal favourites are Sindy doll - I was always a Sindy girl as she was a cool British icon.
'I also adored Glo Worm, even though I was maybe a bit old for it and Simon felt like properly, cutting edge, advanced technology when it came out - it was literally the soundtrack of Christmas in the 80s.'
Senior Hamleys buyer Karen Dennett said she particularly remembered toys where stocks were under severe pressure due to unforeseen demand and unusually had to be restricted to one per customer.
She said: 'It was mayhem at times with toys like the Frozen Singing 'Let it Go' Doll - we were getting them rush air freighted in to try to satisfy demand.
A Barbie doll, pictured left, and a Tamagotchi, pictured right
Monopoly (pictured), the Tamagotchi virtual pet, the Nintendo Game Boy and the Furby also made the list
The toy store made a 'hero' list with the help of industry buyers to mark its 265th birthday and included toys that had cultural impact, enduring popularity and historical significance. Pictured, a Furby
'I remember me and my brother both getting a Rubik's Cube for Christmas. He solved it super quick, but I was nowhere near solving it, so I remember peeling the coloured stickers off to allow me to look like I had managed it.'
Ms Kay said it was difficult to determine what made a toy popular, but said: 'You can never underestimate the power of togetherness created around some of the big-sellers - those toys that bring people of all ages together - get families around a table talking, playing, challenging, maybe even cheating. Monopoly would be nothing without the competitive family battles that emerge.
'We also mustn't forget that simplicity is often key - the joy of cuddling a doll or storytelling with an action figure or a superfast Hot Wheel car.
'Combined with a good dose of jeopardy and you have something truly memorable - think Operation or Kerplunk, Jenga or Buckaroo - they are so simple.
'I used to panic trying to balance the boot in Mousetrap and be terrified of the noise Operation would make when I got it wrong or just burst with panicky laughter when the Jenga tower finally wobbled and collapsed. Toys like that will last forever.'