All safari zones of Ranthambore national park remain open from 1st October to 30th June. From 1st July to 30th September only zones 6 to 10 remain open, which is also subject to rains and road conditions.
Best time to visit Ranthambore national park totally depends on what you expect from the park. Summers is usually a great time to spot tigers as the natural water resources dry out and animals in the forest depend on manmade watering holes for fulfilling thrust. So watering holes become the sure shot places to have good wildlife spotting during summers. But as the heat increases, it becomes tough for the visitors as well to do safaris during that period as well. So generally during those months you will find wildlife photographers and wildlife enthusiasts mostly going to the park, who look for good pictures of wildlife.
Otherwise general tourists would like to visit Ranthambore national park during mostly between 1st October and 30th April. That is the time when wildlife spotting is good and weather conditions are appropriate.
Now a days in monsoons as well, few gates of Ranthambore national park remain open and it is good time for those who wish to relax and enjoy in the green surroundings. A lot of corporate groups and conferences can be seen visiting Ranthambore national park during this period.
To summarize we can say Ranthambore National Park has become all year round destination, all depends upon what you are looking at and what you expect from the destination.