Jimmy was born in Bromsgrove and grew up and lived in Redditch, Worcestershire. Jimmy started playing football at a young age. He was educated at Arrow Vale High School from 1995 to 1998. He joined Manchester United as a trainee in July 1999 and turned professional at the end of the following month. In January 2001, he was sent on loan to Royal Antwerp for four months where he only played in four games, all as a substitute. He made his only first-team appearance for United in the Worthington Cup Third Round defeat against Arsenal at Highbury on 5 November 2001. United lost this game 4–0.
Jimmy was loaned to Swindon for three months in the 2002–03 season, making 15 appearances for the Division Two side, scoring three goals, although it was not enough to bring anything better than a mid-table finish for Andy King's side. Davis was keen on accepting an offer to extend his deal, but United manager Alex Ferguson recalled him. His last game for Swindon Town was on 9 November 2002. After returning to Old Trafford, he was on the bench for United's UEFA Champions League tie away to Deportivo La Coruna just before the end of 2001–02. He then joined Watford on a season's loan in August 2003.
Jimmy was killed in a car crash on the M40 motorway in the early hours of 9 August 2003. He crashed his BMW into a truck and was pronounced dead at the scene. The truck driver suffered minor injuries. The accident occurred just hours before Watford were due to open their season with a match against Coventry City. The Watford board of directors announced later that morning that the match was postponed due to "tragic circumstances beyond their control", though they did not announce Davis' death for another few hours. His funeral took place at Redditch Crematorium, with the Manchester United team in attendance.
The subsequent inquest reported that Davis was more than twice over the legal drink-drive limit and it was believed that he had been driving at speeds of up to 120 mph when losing control of his car when he fell asleep at the wheel. The inquest returned a verdict of accidental death.
A few days after his death, Swindon dedicated their 4–0 win over Notts County to the young player, with Davis's mother making a speech in front of the Swindon fans before the kick-off. Additionally, Swindon Town took part in a memorial match with his local club Redditch United; Swindon won 2–1 with Sam Parkin scoring the goals. Manchester United paid tribute to him during their 2003 FA Community Shield victory against Arsenal, with both teams wearing black armbands during the match. United also paid tribute to him after their victory in the 2004 FA Cup Final, when after the final whistle and before the presentation they changed into shirts printed with Davis's name and squad number, 36, on the back..