Ok, did some homework here. These are the known center-fire calibers that use bullets close to .223:
Current/Common
1. 22 Hornet (5.6x36R mm)
2. 218 Bee
3. 222 Remington
4. 223 Remington, 5.56x45 NATO
5. 22 PPC
6. 225 Winchester
7. 22-250
8. 220 Swift
9. 22 Accelerator (.30-30 and .30/06 adaptation)
Obsolete
10. 219 Zipper
11. 22-15-60 Stevens
12. 22 Extra Long Centerfire
13. 22 Winchester Center Fire
14. 222 Remington Magnum
15. 22 Savage High Power
Wildcats
16. 22 K-Hornet
17. 22/R-2 Lovell
18. 218 Mashburn Bee
19. 223 Ackley Improved
20. 22 Waldog
21. 22 Dasher
22. 219 Donaldson Wasp
23. 22 BR Remington
24. 22-250 Ackley Improved
25. 220 Wotkyns-Wilson Arrow
26. 220 Weatherby Rocket
27. 22 Cheetah
28. 22 Newton
29. 228 Ackley Magnum
Specialty
30. 226 JDJ
31. 224 Weatherby Magnum
Handgun
32. 5.45x18 Soviet
33. 221 Remington Fireball
Other (Military)
34. 5.7x28 FN
35. 5.45x39 Russian
European
36. 5.6x33, 5.6x33R Rook and Tesching
37. 5.6x50/R Magnum
38. 5.6x57mm/R RS
39. 5.6x61/R MM Vom Hofe Super Express
These are from Cartridges of the World by Frank C. Barnes and various Internet sources.