Sure, I have compiled a list of NFL quarterbacks who were picked in the top 10 picks in the first round since 2003:
1. 2003 - Carson Palmer (#1) by Cincinnati Bengals
2. 2004 - Eli Manning (#1) by San Diego Chargers (was immediately traded to the New York Giants)
3. 2005 - Alex Smith (#1) by San Francisco 49ers
4. 2006 - Vince Young (#3) by Tennessee Titans, Matt Leinart (#10) by Arizona Cardinals
5. 2007 - JaMarcus Russell (#1) by Oakland Raiders
6. 2008 - Matt Ryan (#3) by Atlanta Falcons
7. 2009 - Matthew Stafford (#1) by Detroit Lions, Mark Sanchez (#5) by New York Jets
8. 2010 - Sam Bradford (#1) by St. Louis Rams
9. 2011 - Cam Newton (#1) by Carolina Panthers, Jake Locker (#8) by Tennessee Titans, Blaine Gabbert (#10) by Jacksonville Jaguars
10. 2012 - Andrew Luck (#1) by Indianapolis Colts, Robert Griffin III (#2) by Washington Redskins, Ryan Tannehill (#8) by Miami Dolphins
11. 2013 - EJ Manuel (#16) *No QB selected in top 10
12. 2014 - Blake Bortles (#3) by Jacksonville Jaguars
13. 2015 - Jameis Winston (#1) by Tampa Bay Buccaneers, Marcus Mariota (#2) by Tennessee Titans
14. 2016 - Jared Goff (#1) by Los Angeles Rams, Carson Wentz (#2) by Philadelphia Eagles
15. 2017 - Mitchell Trubisky (#2) by Chicago Bears, Patrick Mahomes (#10) by Kansas City Chiefs
16. 2018 - Baker Mayfield (#1) by Cleveland Browns, Sam Darnold (#3) by New York Jets, Josh Allen (#7) by Buffalo Bills, Josh Rosen (#10) by Arizona Cardinals
17. 2019 - Kyler Murray (#1) by Arizona Cardinals, Daniel Jones (#6) by New York Giants, Dwayne Haskins (#15) *No QB selected in top 10
18. 2020 - Joe Burrow (#1) by Cincinnati Bengals, Tua Tagovailoa (#5) by Miami Dolphins, Justin Herbert (#6) by Los Angeles Chargers
19. 2021 - Trevor Lawrence (#1) by Jacksonville Jaguars, Zach Wilson (#2) by New York Jets, Trey Lance (#3) by San Francisco 49ers, Justin Fields (#11) *No QB selected in top 10
This is just a quick summary, so if you'd like to know more about how each quarterback's career has worked out or any other details, feel free to ask!