What did you start the game with? I started with low tech and 1 planet. I'm on turn 169 and I have 223 ships. 38 of them are enemy ships I converted in the Last two turns with my allegiance subverters. I've got 51 cruisers, 15 battle cruisers with damaging weapons, 66 battle cruisers with allegiance subverters, and a whopping 2 light carriers. I'm only about 6 or 7 turns away from having 3 battle moons (10000kt ships).
In conclusion, my navy tends to get rather large (especially with enemy ships
).