You could justify buying this game on the single player aspect alone. I owned Burnout on my old Xbox and enjoyed it immensly from start to finish. But Revenge manages to raise the bar even further and not only improve on the single player game in just about every area but also present one of the most cohesive and intense Live games available on the 360.
Criterion has implemented a simple yet effective 'revenge' system which tracks all the people you've crossed paths with in previous races. So if you've pummled some poor guy into the wall a number of times you'll be pride of place at the top of his revenge hit list the next time he joins a race that you're in.
At the start of each race you can instantly see who you've taken down before (denoted by a green exclamation mark) and those who are looking to settle the score with you (denoted by a green exclamation mark). Just to hammer the point home there's a quick 'fly by' of the grid highlighting the people looking to settle a score with you and those you should be looking to ram into the nearest bus.
I would highly reccomend that newbies to the Burnout series finish the single player game before venturing online (unless you've got a lot of patience). Almost all of the player created sessions are played with the fastest available cars, so the sheer pace of the races can be punishing to a new comer.
All in all, even if you have a passing interest in racing games - give Burnout Revenge a try. Singleplayer is brilliant - but it's the multiplayer mode that really shines.