race games with free roam

Need for speed most wanted (original version)
Best Nfs ever

Fuel, Burnout Paradise, Need for Speed Underground series (dunno if the newer NFS has them).

Need for speed

SRS

Test Drive Unlimited 2

Drift City.

Euro Truck Simulator 2 =)

If you like tuning and cops try NFS MW(original), if you like post apocalyptic racing then FUEL, or if you want to race with exotic cars try Test drive unlimited 1-2.

Midtown Madness 2, I dunno why but there is cars and free running and I love it!

Burnout Paradise comes to mind. Not a lot of car customization other than paint/skins but it has everything else you mentioned. It was recently in the Humble Origin bundle so you may be able to get it for cheap or win it somewhere (especially if you don't mind it being an Origin key).
You drive around a pretty big city and there's race events all around the city that you can start by stopping at certain traffic lights. There's also lots of "collectibles" around the city like objects you can smash, billboards to smash through, big jumps and even some hidden areas.

Burnout Paradise, you can probably get it in a trade for cheap since it was in the Humble Origin Bundle.

Driver SF

I don't play them very often, but I have Driver: San Francisco. Doesn't meet all you're looking for but it can be open world.

NFS Undercover? It's free world, and I am sure you can customize vehicles and what not, I was really enjoying it, until my car got confiscated.

Carmageddon.

Test Drive Unlimited 2. Unfortunately due to bugs not running on my PC anymore and Atari Support gives a shit

Nfs:mw. I've heard they wanted to make a sequel, but it was canceled and nobody heard about that ever again.

midnight club LA is free roam, but my fav racing game is forza 4

You block the way anyway...

nfs world (free2play)

burnout paradise

Burnout is pretty fun.

i was in the same situation a while ago. i 've tried a lot of racing games to find a good one.
Need for speed :most wanted , is one of the latest games like this.Its graphics are badass but the only thing i dislike on it ,is that there is not that much of customazation for the cars.

I recently bought midnight club los angeles for my ps3 just because i liked the gameplay and that there is a lot of addons for the cars ,comparing it to nfs and burnout paradise.
Dunno if there is a pc version but check it out ;)

test drive unlimited 2 is a mmorg - massively multiplayer online racing game - where it is free-roaming with other real players crusing around an open-world map