Four cricketers have scored more than 1000 runs in ICC Cricket World Cup tournaments. The four players with more than 1000 runs in World Cup history were:

1. Sachin Tendulkar (India) : Sachin Tendulkar, often regarded as one of the greatest batsmen in cricket history, scored a record 2,278 runs in six Cricket World Cup tournaments from 1992 to 2011. He is the highest run-scorer in World Cup history.

2. Ricky Ponting (Australia) : Ricky Ponting, the former Australian captain, is another cricketing legend. He scored 1,743 runs in five World Cup tournaments from 1996 to 2011. Ponting played a pivotal role in leading Australia to multiple World Cup victories during his captaincy.

3. Kumar Sangakkara (Sri Lanka) : Kumar Sangakkara, the elegant Sri Lankan batsman and former captain, accumulated 1,532 runs in four World Cup tournaments from 2003 to 2015. His consistency and batting prowess made him a key figure for Sri Lanka in World Cup competitions.

4. Brian Lara (West Indies) : Brian Lara, one of the most stylish left-handed batsmen in cricket history, scored 1,225 runs in five World Cup tournaments from 1992 to 2007. While West Indies struggled in some of those tournaments, Lara's performances were often a highlight.

These four players achieved remarkable milestones in World Cup cricket, showcasing their skills and consistency on the grand stage of international cricket. Their contributions to their respective teams' successes and their records in World Cup tournaments are celebrated by cricket fans worldwide. However, please verify the latest statistics to ensure accuracy given that new World Cup tournaments may have occurred since my last update.