1. Fallout 2. My all-time favorite game, I have finished it probably 20+ times. A true classic. Everything just clicks.
2. Fallout Tactics. I rank this one second, it's actually a really good, overlooked game! Although there's not so much freedom when it comes to roleplaying. If you want to finish the game, diplomats aren't much help since you really need all those heavy gunners and energy weapon specialists. However, the combat is the most satisfying of them all, and the different mission objectives are pretty interesting throughout. Plus, bug-squashing is SOOO satisfying!
3. Fallout New Vegas. The game F3 should've been. In my heart I still hope they would've kept the old look and not go into 1st person at all, but despite that, it's still a really good game. Worthy of the Fallout name, for sure. Interesting quests and the Mojave looks really good.
4. Fallout 3. While it's debatable whether this is worthy of the Fallout name or just an "Oblivion with guns", it's still a good game and offers many hours of A+ gameplay. When it comes to the Fallout series though, there are much better options available in my opinion.
5. Fallout 1. Granted, it started it all so maybe it should be higher on my list, but the fact is, Fallout 1 has aged the most poorly of all Fallouts. Especially when compared to Fallout 2, which has so much more of everything. F1 is pretty linear, there's not many places of interests, the interface is a little clumsy, especially with companion trading, and the quests are a little shallow. The game is still worth playing, that's for sure, but first-timers shouldn't begin with this.
---Dishonorable mention----
Fallout BOS. I don't consider this one part of the Fallout saga at all. It's best be forgotten entirely.