Yes, all iMacs (for the last 3 or 4 years) come standard with wifi built-in. The last two years, that wifi card supports 802.11b, g, a, and n.
Your present G router will work just fine, but only at the G speeds. If you want the much faster N,(and somewhat greater range as a bonus), then you will need to provide an N-class router. Apple's Airport Express, or Extreme/Time Capsule routers will certainly work, but are not required. You can replace with another brand, if you like...