According to Andrew Powell-Morse, from 2009-2013, the New York Jets have been the fourteenth most penalized franchise in the National Football League, with a total of 505. Incredibly, if you were to remove that one twenty-flag performance against the Buffalo Bills, the team would drop to the eighteenth most penalized franchise. Overall, they're pretty average when it comes to being penalized.
When it comes to actual yards lost due to the penalties, the Jets have lost 4,193 yards, or eighteenth most in the league. That's an average of nearly 54 yards lost per game (this does not include the recent game against the Cleveland Browns, or obviously the upcoming game against the Miami Dolphins).
Of the most frequently penalized players, current Jets Antonio Cromartie (32) and Willie Colon (30) are on the list, however Cromartie came to the team in 2010 and Colon in 2013, so some of those penalties come from their previous teams. Of the top twenty-one penalized players, four are defensive backs and ten are offensive linemen, so Cromartie and Colon aren't too surprising, just based on their position, which are penalized more often than any other group.
However, not all penalties go against a team... some go in favor of the Jets. The Jets have received 493 penalties in their favor, good for nineteenth in the league, and a total of 4,126, which is more than those coming against the team. On the whole, however, the Jets are an average team when it comes to penalties for and against, when compared to the rest of the league.