My list of "capital cities" visited coincides nearly perfectly with "countries visited":
Americas
1. Washington DC (USA)
2. Ottawa (Canada)
3. Santiago (Chile)
4. Port of Spain (Trinidad and Tobago)
Europe
5. Paris (France)
6. London (UK)
7. Madrid (Spain)
8. Copenhagen (Denmark)
9. Rome (Italy)
10. Monte Carlo (Monaco)
11. Brussels (Belgium)
12. Amsterdam (Netherlands)
13. Vatican (Vatican)
Asia
14. Bangkok (Thailand)
15. Taipei (Taiwan)
16. Beijing (China)
17. Singapore (Singapore)
18. Tokyo (Japan)
19. Vientiane (Laos)
Also been to Hong Kong.
The only state that I've been to whose capital I haven't been to is Germany, and that's only because of a very quick cross-border excursion from Denmark (and I mean "very" in the order of 5 minutes or so, so in some respects it doesn't even count); and Berlin is high on my list of next places to visit so once that's done the list will coincide perfectly.