The like of Luis Suarez, Daniel Sturridge and Philippe Coutinho immediately spring to mind.
But they have certainly had to get through some turkeys as well.
Names like Stewart Downing, Andy Carroll and Alberto Aquilani immediately spring to mind - while there are plenty of others as well.
One such name - who arrived in the ill-fated Roy Hodgson era - was Danish international Christian Poulsen.
The defensive midfielder came with plenty of pedigree.
He had spent time at Schalke, Sevilla and Juventus before making a £4.5 million move to Anfield in 2010 - but his two years on Merseyside were largely forgettable.
He went on to play for Evian and since 2012 has been playing for Ajax - but this summer will be looking for new employment once again.
It has been announced today that the Liverpool flop will leave Ajax in the summer.
"It was a difficult decision because I'm really enjoying myself at Ajax. My family is too. We think that it's a nice club with great people. We wanted to think carefully about it. My decision was taken with my brains instead of my heart - if I had gone the latter, then I would have re-signed. But I want a nice way to say goodbye and I do that now, as a fit player with another championship."
Poulsen has recently lost his regular spot in the Ajax first-team - and wants to finish his career with a bang.
At the age of 34 he is fast approaching the end of his career - and the likely story is he will return to Denmark to finish his career, with former club FC Copenhagen a potential location.
We think a return to Liverpool is however very unlikely.