Well, it depends.
What Mazda recommends is Mazda Moly Oil, which is an ultra high moly oil manufactured by Idemitsu. While it's fine oil, I don't really see the point of buyiing the Mazda branded oil when you can get Idemitsu EcoMedalist Moly (make sure you get the moly version, there are EcoMedalist blends with far less) for less money and it is, near as anyone an tell, the same oil.
However, I don't really like the Idemitsu much either. It wasn't badly priced for a while, but now that people have caught on the prices have gone way up to $40+ for a 5qt jug, or $8 and some change a qt. That's less than Mazda, but still pretty expensive.
If you want to go with a high moly oil, what I'd actually recommend is Toyota Genuine oil, which is very similar to Mazda/Idemitsu oil (it also has an enormous slug of Moly) but is considerably less expensive than either. Currently it's sitting on Amazon at about $7.20 a qt, although you need to buy 12qts to get that deal. The price is higher than it was last I checked, and it does vary quite a bit so keep your eyes open. There are a few differences in the formula vs Mazda, but ultimately it's a quality oil made by a major manufacturer (Exxon-Mobil) to similar specs for the same reasons.
That said, I don't run any of those in my Mazda. While a high moly oil isn't going to hurt, and it does bring some benefits (mostly in MPGs), it's really not necessary and it's quite expensive. You may get fractionally better MPGs, but you will get the same life out of your engine with any quality synthetic as you will with the mega-bucks mega-moly oils. It's worth pointing out that in my owners manual, right next to the recommendation for Mazda Moly oil, is a recommendation for Castrol, followed up by a statement that any SN rated oil is acceptable and Mazda will warrant their use. Castrol does not make a high moly oil, so it leads me to believe that the high moly is not necessary for proper function of your engine. Mazda wouldn't recommend, let alone warrant, low moly Castrol otherwise.
Right now, I'm running Pennzoil Platinum 0W20 in mine because it was on sale for a good price. When it comes time to change, I'll probably get whatever's a good deal at the time and not worry about it. Mobil, Magnatec, Quaker State UD, black bottle Castrol, Pennzoil, Valvoline, even most store brands, it's all fine. It's your car and your money, so you can do whatever you want, but IMO you'll be just fine with any synthetic oil from a reputable manufacturer changed on schedule.