This is a dynamic list and may never be able to satisfy particular standards for completeness.
World records
1. Most (FIFA) Ballons d'Or: 5 (2009–12, 2015) (shared with Cristiano Ronaldo)
2. Most consecutive Ballons d'Or: 4
3. Youngest two-time, three-time, four-time and five-time Ballon d'Or winner: 23, 24, 25 and 28 years old
4. Guinness World Record as top goalscorer for club and country in a calendar year: 91 goals in 2012
5. Most goals in a calendar year (including club friendlies): 96 goals in 2012
6. Top goalscorer in all club competitions in a calendar year: 79 goals in 2012
7. Top goalscorer in a club season: 73 goals in 2011–12
8. Longest goalscoring run in a domestic league: 21 matches, 33 goals in 2012–13
9. Only player to have won more than one FIFA Club World Cup Golden Ball
10. Only player to have won more than one FIFA Club World Cup Final Most Valuable Player award
11. Only player to score more than 40 goals in 10 consecutive calendar years
12. Only player to score more than 40 goals in 10 consecutive seasons
13. Only player to score in 6 different club competitions in a calendar year twice: 2011 and 2015
14. Only player to score and assist in 6 different club competitions in a calendar year: 2011
15. Only player to score 60+ goals in all competitions in 2 consecutive seasons: (2011/12 and 2012/13)
16. First player ever to score consecutively against all teams in a professional league
17. Most appearances in the FIFPro World XI: 12 times (2007–2018) (shared with Cristiano Ronaldo)
18. Most appearances on a video game cover by a Football player: 10
Continental records
Europe
1. All time top scorer in top 5 european leagues: 419 goals
2. Most official goals for a single club in Europe's top 5 leagues: 602 goals
3. Most goals in a European Cup/Champions League game: 5 goals (shared with 13 other players)
4. Most European Golden Shoe awards: 6
5. Most hat-tricks scored in the UEFA Champions League: 8 (shared with Cristiano Ronaldo)
6. Most goals scored in the league in one season: 50
7. Youngest player to make 100 appearances in the UEFA Champions League: 28 years, 84 days in 2015
8. Top goalscorer in the UEFA Super Cup: 3 goals (shared with Arie Haan, Oleg Blokhin, Gerd Müller, Rob Rensenbrink, François Van der Elst, Terry McDermott, and Radamel Falcao)
9. Most appearances in the ESM Team of the Year: 10 (2006, 2008–2013, 2015–2017)
10. Fastest player to reach 100 UEFA Champions League goals (123 games)
11. Fastest player ever to reach 300 goals in Europe's top 5 leagues (334 games)
12. First player to win UEFA Goal of the Season award for two consecutive years: in 2015 and 2016
13. Most UEFA Champions League group stage goals: 66 goals
14. Most goals scored for a single club in UEFA Champions League: 110 goals
15. Youngest player to score 50 Goals in the UEFA Champions League
16. Youngest player to reach 100 appearances in the Champions League
17. Youngest player ever to score 400+ goals for a single European club (27 years and 300 days)
Americas
1. Top assist provider in Copa América: 11 assists
2. Most goals in CONMEBOL World Cup Qualifiers: 21 goals (shared with Luis Suárez)
3. Most goals scored by a substitute in a Copa America Match: 3
Spanish records
1. Best Player in La Liga awards: 8 (2009, 2010, 2011, 2012, 2013, 2015, 2017, 2018)
2. Most Best Forward in La Liga awards: 9 (2009, 2010, 2011, 2012, 2013, 2015, 2016, 2017, 2018)
3. Top goalscorer in La Liga: 419 goals
4. Top assist provider in La Liga: 166 assists
5. Top goalscorer in the Supercopa de España: 13 goals
6. Top goalscorer in a La Liga season: 50 goals in 2011–12
7. Most braces scored in La Liga: 105
8. Most hat-tricks scored in a La Liga season: 8 in 2011–12 (shared with Cristiano Ronaldo)
9. Most teams scored against in a season: 19 in 2012–13 (shared with Ronaldo Nazário and Cristiano Ronaldo)
10. Most La Liga Appearances by a foreign player: 450 matches
11. Only player to score consecutively against all opposition teams in La Liga: 19 matches, 30 goals in 2012–13
12. Most league home goals in a season (38 games, 19 home games): 35 (2011–12)
13. Most league away goals in a season (38 games, 19 away games): 24 (2012–13)
14. Most league matches scored in a season (38 games): 27 (2012–13)
15. Most league home matches scored in a season (38 games): 16 (2011–12)
16. Most league away matches scored in a season (38 games): 15 (2012–13)
17. Most opponents scored against in La Liga history: 37
18. Most consecutive away league matches scored in: 13 (20 goals from matchday 8 to matchday 33, season 2012–13)
19. Only players to be top goalscorers and top assist providers in the same season: Luis Suárez (2015-16), Lionel Messi (2017-18)
20. Most stadiums scored at: 36
21. First player to score in 15 consecutive seasons
22. Only player to score 20+ goals in 10 consecutive seasons
23. Only player to score 30+ goals in 7 different seasons
24. Only player to score 10+ goals in 13 consecutive seasons (from 2006-07 to 2018-19)
25. First player to reach 300 La Liga goals
26. First player to reach 350 La Liga goals
27. First player to reach 150 La Liga assists
28. Youngest player to score 200 goals in La Liga: 25 years and 7 months in January 2013
29. Most La Liga titles won by a Non Spanish individual: 10 (all with Barcelona)
30. Most Copa Del Rey finals scored in: 6 (2009, 2012, 2015, 2017, 2018) (shared with Telmo Zarra)
31. Most assists provided in Copa Del Rey finals: 6 (1 in 2009, 2 in 2016, 1 in 2017, 2 in 2018)
32. Most goals scored from direct free kicks: 28
Argentine records
1. Argentina all-time top goalscorer: 65 goals
2. Top goalscorer for Argentina in a calendar year: 12 goals in 2012 (shared with Gabriel Batistuta)
3. Only Argentina player to score against every CONMEBOL nation
4. Youngest player to play for Argentina in a FIFA World Cup: 18 years, 357 days in 2006
5. Youngest player to score for Argentina in a FIFA World Cup: 18 years, 357 days in 2006
6. Youngest player to reach 100 caps for a country under CONMEBOL's jurisdiction: 27 years, 361 days in 2015
Club records
Barcelona
1. Top goalscorer in El Clásico: 27 goals
2. Top goalscorer in the Derbi barceloní: 25 goals
3. Top goalscorer in official competitions: 602 goals
4. Top goalscorer including friendlies: 637 goals
5. Top goalscorer in the UEFA Champions League: 112 goals
6. Top goalscorer in European competitions: 115 goals
7. Top goalscorer in international competitions: 120 goals
8. Most hat-tricks scored in all competitions: 45
9. Most hat-tricks scored in La Liga: 33
10. First player to be top goalscorer in four, five and six La Liga seasons (2009–10, 2011–12, 2012–13, 2016–17, 2017–18, 2018-19)
11. Most titles won with the team: 34
12. Most matches won with the team: 476 (equalled on 3/13/2019)