Pros: Today many Xbox 360 games can be collected (as used specimens) at affordable prices. The quality of “360” games still compares pretty nicely with that of games for “eighth-generation” consoles (e.g., Xbox One or PlayStation 4).
Cons: Think twice about buying any “downloadable” games (via Xbox LIVE) for your Xbox 360 console. (I’ll explain why below.)
 

Preface  (Feel free to skip ahead to the list of games)
It wasn’t till 2013 that I got my first Xbox 360 console. By having waited so long after the console’s 2005 advent, I was able to buy three brand-new “Slim” consoles (in my preferred special-edition white hue) – each including a white, wireless controller – for scarcely more than what I would’ve originally paid for just one unreliable “deluxe” console. [Some might wonder why I bought more than just one Xbox 360 specimen. Well, on the one hand, I like knowing that I’ll almost certainly be able to play at least one of those consoles for the next two decades, i.e., years after one or two of ‘em have probably stopped working. On the other hand, I could end up selling one or both of the “backup” consoles someday as “still new, tested” specimens.]
Moreover, waiting so long to leap aboard the “360” bandwagon enabled me to purchase most of my compatible games at significantly discounted prices.

Note that I do have three key criteria determining (or at least influencing) which games ended up on the list (and in my personal collection).
First, titles like “Driver;” “Grand Theft Auto,” and “Fast and Furious” [which I myself neither play nor collect] are primarily role-playing, not racing, games. Thus I generally don’t include such titles on this list.
Second, excessively puerile/adolescent/cartoony graphics, audio or themes normally don’t appeal to this adult gamer; so, you generally won’t find such titles on this list. [But I’ve no such compunctions about certain seemingly universally beloved kart-racing titles – like the ones involving “Sonic” – that don’t unduly annoy adult sensibility.]

Third, if a game absolutely forces me to be connected to the Internet in order to play it, I will neither buy nor endorse that game! [Hence you won’t find The Crew (a late-2014 release) on my list.]
Note:  I’m American. Unsurprisingly, my below list comprises (with two qualified exceptions, i.e., F1 2013 and WRC 2) only NTSC editions. And some games may bear different titles (or perhaps weren’t released) in other world regions. [Consult Wikipedia for details.]
Finally, my general intention isn’t to discuss any particular game below; but the simple fact that these are the titles that made my list means each somehow merits a passing grade (though in several instances just a “D+”). So, use the following list judiciously,  perhaps consulting pertinent reviews, articles or videos at the worthy Amazon, eBay, IGN, Wikipedia and YouTube to decide for yourself if a certain title belongs in your collection.

NOTE:  I’ve divided my overall list into three shorter lists. The first list comprises ordinary retail (on-disc) Xbox 360 games. The second list comprises several “downloadable” Xbox 360 games. And the third list comprises retail on-disc games that were released for the original (2001) Xbox console yet are compatible with any North American Xbox 360 console having an official, Microsoft-brand hard drive.
COLLECTIBLE RETAIL XBOX 360 “RACING” GAMES RELEASED ON DISC (DVD) IN NORTH AMERICA:
(To view a picture of a particular game, click its “See it at Amazon” link.)

1. Baja: Edge of Control
   
2. Blood Drive       
3. Blur       
4. Burnout Paradise       
5. Burnout Revenge      
6. Dirt      
7. Dirt 2      
8. Dirt 3      
9. Dirt Showdown      
10. F1 2010      
11. F1 2011      
12. F1 2012      
13. F1 2013            [Note: This particular title’s British (PAL) edition is “region-free,” i.e., fully compatible with North American (NTSC) consoles. (As of this writing, you can order via Amazon.com either the PAL edition [the one I myself own] or the much pricier NTSC equivalent.)]
14. F1 2014      
15. F1 Race Stars      
16. Fatal Inertia      
17. Flat Out: Ultimate Carnage      
18. Forza Horizon      
19. Forza Horizon 2      
20. Forza Motorsport 2      
21. Forza Motorsport 3      
22. Forza Motorsport 4      
23. Fuel      
24. Full Auto      
25. Grid       
26. Grid 2      
27. Grid Autosport (“Black Edition”)      
    [Note:  Might as well get this expanded “Black” edition (which includes an extra car, etc.), since — ironically — it’s available for less than the cost of the “Standard” edition.]
28. Hot Wheels: Beat That      
29. Import Tuner Challenge      
30. Indianapolis 500 Evolution      
31. Jimmie Johnson’s Anything with an Engine      
32. Juiced 2: Hot Import Nights       
33. Mayhem 3D      
34. Midnight Club: Los Angeles – Complete Edition      
35. Monster Jam      
36. Monster Jam: Path of Destruction      
37. MotoGP 06      
38. MotoGP 07      
39. MotoGP 08      
40. MotoGP 09/10      
41. MotoGP 14      
42. MUD: FIM Motocross World Championship      
43. MXGP: The Official Motocross Videogame      
44. MX vs. ATV Alive      
45. MX vs. ATV Reflex      
46. MX vs. ATV Untamed      
47. Mx vs. ATV: Supercross      
48. Nail’d      
49. NASCAR 08      
50. NASCAR 09      
51. NASCAR The Game 2011      
52. NASCAR: Unleashed      
53. NASCAR The Game: Inside Line      
54. NASCAR ’14     
55. Need for Speed: Most Wanted (2005)      
56. Need for Speed: Carbon (2006)      
57. Need for Speed: ProStreet (2007)      
58. Need for Speed: Undercover (2008)      
59. Need for Speed: Shift (2009)      
60. Need For Speed: Hot Pursuit (2010)      
61. (Need For Speed) Shift 2: Unleashed (2011)      
62. Need for Speed: The Run (2011)      
63. Need for Speed: Most Wanted (2012)      
64. Need for Speed: Rivals (2013)      
65. PocketBike Racer     
66. Project Gotham Racing 3      
67. Project Gotham Racing 4      
68. Pure      
69. Race Pro      
70. Ridge Racer 6      
71. Ridge Racer Unbounded      
72. SBK Superbike World Championship      
73. SBK X: Superbike World Championship      
74. Score International: BAJA 1000      
75. Sega Rally Revo      
76. Ski Doo: Snowmobile Challenge      
77. Sonic and All-Stars Racing Transformed      
78. Sonic & Sega All-Stars Racing      
79. Split/Second      
80. SSX      
81. Stuntman: Ignition      
82. Test Drive: Ferrari Racing Legends      
83. Test Drive Unlimited       
84. Test Drive Unlimited 2      
85. World of Outlaws: Sprint Cars      
86. WRC 2: FIA World Rally Championship         [Note: Although this 2011 game wasn’t released in North America, its British “PAL” edition is (unlike all other Xbox 360 PAL editions in the WRC series) “region-free” and thus can be played on North American “NTSC” Xbox 360 consoles. I ordered my preowned copy via Amazon.com’s link to their “United Kingdom” website for $14.89 USD (including shipping from England to USA).]

DOWNLOADABLE RACING GAMES
Note that several excellent racing games are also available – strictly as downloads – via Microsoft’s “Xbox Live.” Apart from Daytona USA (whose demo wasn’t quite impressive enough to convince me to buy the full game), the following three titles are noteworthy (and I enjoy them all very much):

1. Hydro Thunder Hurricane
2. Jeremy McGrath’s Offroad
3. SkyDrift

[However, if lasting value matters to you, heed my warning (in the addendum below) regarding buying any downloadable games for your Xbox 360 console!]
“ORIGINAL XBOX” RACING GAMES COMPATIBLE WITH XBOX 360 CONSOLES

Many (but not all!) racing games for the original Xbox console (released in 2001) are likewise compatible with any Xbox 360 console having an official, Microsoft-brand hard drive. [Flash memory/thumb drives don’t work with original-Xbox games; moreover, third-party/generic, non-Microsoft hard drives reportedly won’t work reliably, if at all, so don’t even try that!] Thus I’m also providing the below list of the 43 original-Xbox racing titles that I deem worth keeping in my “360” collection (and which generally look better than ever via my 360 console’s HDMI connection to a modern TV).
[Also note that your Xbox 360 console must initially be online such that Microsoft can download the pertinent “emulation” file allowing your original-Xbox game disc to play via the Xbox 360 system. That emulation file is automatically downloaded and stored on the Xbox 360 console’s hard drive the first time you insert a 360-compatible original-Xbox game disc; thereafter, it won’t be necessary for that Xbox 360 console to be online in order to play that original-Xbox game.]
RETAIL “ORIGINAL XBOX” RACING GAMES RELEASED ON DISC IN NORTH AMERICA (AND COMPATIBLE WITH NORTH AMERICAN XBOX 360 CONSOLES):

1. 4×4 Evo 2      
2. APEX      
3. ATV Quad Power Racing 2      
4. Auto Modellista         [Note: Be aware that the “car handling/steering” in this game (not only in this Xbox but also the virtually identical GameCube and PS2 editions, which I’ve likewise collected) is notoriously touchy/difficult! “Casual/occasional” gamers would do well to skip this title.]
5. Burnout       
6. Burnout 2: Point of Impact      
7. Burnout 3: Takedown      
8. Colin McRae Rally 04      
9. Colin McRae Rally 2005      
10. F1 2001     
11. Flat Out      
12. Ford Mustang Racing    
13. Ford Vs. Chevy      
14. Forza Motorsport      
15. Grooverider: Slot Car Thunder      
16. Hot Wheels: Stunt Track Challenge      
17. IHRA Professional Drag Racing 2005      
18. IHRA Drag Racing: Sportsman Edition          [Note: This game typically costs well over 20 dollars – not because it’s particularly good (it isn’t!) but simply because it’s relatively rare. Thus I chose to settle for the basically identical PS2 edition, which is dirt-cheap.]
19. IndyCar Series 2005      
20. Maximum Chase      
21. MotoGP      
22. MotoGP 2      
23. MTX Mototrax      
24. MX Unleashed      
25. MX vs. ATV Unleashed      
26. MX World Tour featuring Jamie Little      
27. NASCAR Thunder 2002      
28. NASCAR Thunder 2003      
29. NASCAR 06: Total Team Control      
30. Need for Speed Underground 2      
31. Outrun 2      
32. OutRun 2006: Coast 2 Coast          [Note: This game typically costs at least 30 dollars because it’s relatively rare. Thus I chose to settle for the basically identical PS2 edition, which can be found for well under 10 dollars.]
33. Project Gotham Racing      
34. Project Gotham Racing 2      
35. Pro Race Driver      
36. Quantum Redshift      
37. Rallisport Challenge      
38. SEGA GT 2002      
39. Speed Kings      
40. SSX 3      
41. SX Superstar      
42. Test Drive (2002)      
43. Test Drive: Eve of Destruction      

Note: The following two “360-compatible” original-Xbox titles are more “combat-driving” than “racing” games, but they might nonetheless be of interest.
RoadKill      
Starsky And Hutch      
In this vein, the following “360-compatible” original-Xbox title might likewise be of some interest.
SpyHunter 2      
 
Addendum
Warning:  The three downloadable games that I cited above [Hydro Thunder Hurricane; Jeremy McGrath’s Off-Road; and SkyDrift) arguably don’t constitute good long-term value, because once your “primary” console breaks — and Xbox Live support for Xbox 360 is eventually terminated (as Microsoft did in early 2010 for the original Xbox console) — your precious downloads will effectively disappear!
[Note: An acquaintance of mine recently mused that it’s conceivable Microsoft might, upon terminating Xbox 360 support, provide some compensatory means for any past purchaser of such downloaded games to freely play his downloads on Xbox 360 consoles other than his “primary” (original) one. But I believe that’s merely wishful thinking, because past history suggests it just “ain’t gonna happen.”]
Admittedly, “for the time being” I’m still relishing the ninety-five dollars’ worth of superlative games (including some non-racing, “arcade” titles) that I downloaded from Xbox Live. Even so, I’m also increasingly feeling that I impulsively made a ninety-five-buck mistake. And I sure won’t be shelling out for any more such downloads.
*   *   *
You may also enjoy the following:  
The 99 Best RACING Games for Original Xbox
The 292 Best RACING Games for PlayStation 2
The 121 Best RACING Games for PlayStation 1
The 81 Best RACING Games for Original Wii
The 48 Best RACING Games for GameCube