I think GRID Autosport is one of the best Dirt Rally is also! Codemasters making the best Driving and Racing games!

NFS Most Wanted from 2005, also like Split Second + Trackmania Nations/Forever

for motorcycle racing definitely ride 2. i also liked motogp urt 3 although it is 10+ years old, at the time it was the best, now it's a bit outdated.
haven't played much car racing games, but i definitely liked nfs carbon, and new most wanted. hot pursuit 2 from early 2000s was great at the time also.

i loved the need for speed series, probably most wanted

For easy arcade I would choose The Need for Speed or Burnout, for more simulated games, The Crew, Asseto Corsa, Forza.

Need For Speed, got to be!

Burnout Paradise and Flatout series because I love demolition derby type games.

NFS Most Wanted and Hot Pursuit would be a more normal one I loved.

Need for speed underground 2... god this was amazing

Need for Speed Most Wanted is my all time favorite, Dirt Rally close second

Burnout and Need for Speed series is really good after all, bring so much old memories