Every year well over a million wildebeest, with zebra and gazelle alongside, move in a loop between Tanzania's Serengeti and Kenya's Maasai Mara, following the rain and the grass.
The herds usually reach the Mara in July and stay until October. This is when the river crossings happen: thousands of animals gathering on the bank of the Mara River, then going all at once.
Nobody can promise you a crossing. The herds may wait on the bank for hours and turn back. Give yourself at least two full days in the reserve, and three if you can, so your guide has time to be in the right place.
August and September are the busiest and most expensive weeks. Late June and October are quieter, cost less, and the resident lions, cheetah and leopard are there all year.
Outside those months the Mara is still one of the best wildlife areas in Africa. If the migration is not essential to you, January to March has green grass, young animals and far fewer vehicles.