Let's start with an easy one. When Torres made his way to Chelsea for £50m (although there's plenty else to be written about his time at Stamford Bridge), Liverpool decided to spend a large portion of the money on an up and coming striker from Newcastle. He'd been scoring for fun in the Championship and in his one season in the Premier League, so it seemed a good investment at the time.
Seven years later and Carroll is back on Tyneside, having been released by West Ham last season. 6 goals in 44 appearances wasn't a great return for the big man up top, and he left Liverpool after just two years.
Of course, this answer is cheating a little bit. At the same time as signing the Geordie lamppost, Liverpool also signed a controversial Uruguayan, whose time in Anfield was slightly more successful.