I am addicted and try to do three or four every day.
It all starts with the NYT. The Saturday puzzles are indeed the hardest. The LA Times Saturday is also a themeless puzzle, but it's always easier than the NYT. It's a good starting point if you want to work up to the NYT.
The hardest by far is
Stanley Newman's Saturday Stumper.
But we are living in a golden age of crosswords. Independent constructors (i.e., people who publish their own puzzles, as opposed to publishing them through a newspaper) put out puzzles weekly, and the majority of them post their puzzles for free.
Here's a great list, with links. The independent constructors don't have to follow any editorial rules, so their puzzles tend to be funnier, fresher, and more R-rated than the NYT and LAT puzzles.
Here's a great example by one of the best indies, Brendan Emmett Quigley.
The only problem with these constructors' puzzles is that they tend to be hard--ranging from Thursday to Saturday difficulty--so they'd probably be frustrating for beginners.
The best approach is to keep doing the Monday and Tuesday NYT and LAT puzzles. Then try to move deeper into the week.
But if you get hooked, bear in mind that (sadly), your friends don't want to hear about how awesome a certain puzzle was.