Tanzania has more than twenty national parks and you won't see them all. The useful way to think about it isn't park by park, it's circuit by circuit, because the circuits are what decide your flights, your driving and your budget.
The northern circuit
Serengeti, Ngorongoro, Tarangire, Lake Manyara and Arusha National Park, all reachable by road from Arusha. This is the one most people mean when they say Tanzania. It has the highest concentration of animals in the country, it has the migration, and the roads between parks mean you can do the whole thing in a vehicle without a single internal flight.
The trade is company. In July and August the Serengeti plains and the crater floor are busy, and you'll share good sightings. If it's your first safari, take the northern circuit anyway. It's popular because it's extraordinary, not because it's convenient.
The southern circuit
Nyerere, which was the northern part of the old Selous, and Ruaha. Bigger, emptier, wilder, and reached by a short flight from Dar es Salaam rather than a drive. Ruaha has one of the largest elephant populations in East Africa and some remarkable lion viewing. Nyerere has the Rufiji River, which means boat safaris and walking safaris, neither of which the northern parks do as well.
You see fewer animals per hour and you see them almost alone. It's a superb second safari and a slightly risky first one, because a quiet morning in Ruaha is genuinely quiet.
The western circuit
Katavi and the chimpanzee forests of Mahale and Gombe, on Lake Tanganyika. Remote, expensive, flight-only, and unlike anything else. Trekking to habituated chimpanzees on a forested mountainside above a lake is not a safari in the normal sense. Go when you've done the rest, and budget properly for it.
How to choose
First trip, one to two weeks: northern circuit, and don't try to add the south. Second trip, or you've been to Kenya: the southern circuit. Honeymoon or a special occasion: north for a week, then Zanzibar. Photographers and people who hate crowds: south. Chimpanzees: west, and plan around the flight schedule rather than your dates.
Don't combine too much
The commonest planning mistake is bolting a southern park onto a northern trip to tick it off. You spend two travel days and a domestic flight to see a third park when another two nights in the Serengeti would have given you more. Depth beats breadth on every safari we have ever planned. There's more on that in how many days you need, and each park has its own page under destinations.
And the conservation areas
Ngorongoro isn't a national park, which is why it has different rules and a separate fee. It's a conservation area, managed so that Maasai communities can live and graze cattle alongside the wildlife, which is unusual in East Africa and is part of what makes the place what it is. Practically, it means its own permit, its own vehicle rules and a strict time limit on the crater floor.