RE2 really started the trend. Early in the game you have to be careful with enemy encounters because you don't have a lot of ammo to spare. Once you get the shotgun or grenade launcher, the game becomes much easier because you can take out multiple zombies easily. If you're really good with the knife, you can use that to take down a zombie or two to conserve ammo. Late in the game, you get enough ammo were no enemy should pose a threat. RE3 is more of the same. You're careful at the beginning and conserve ammunition, but later on you should be fine. As long as you know how to properly dodge, nothing in that game should cause you problems. They give you too much ammo to mow down everything later in the game. You can even create ammo.
RECV people claim to be too hard but I laugh. Even early in Claire's game, she gets dual pistols. The knife is godly on that game. You can take down even multiple zombies with it. Like RE3, you get too much weapons and ammo especially in Chris's part for anything to be a challenge. I've only played RE0 once but I didn't have any trouble with conserving ammo. Billy was a damn tank. I used Rebecca only for healing.
I actually ran low on ammo a few times during my first RE4 playthrough. Same for RE5 (mostly because of Sheva). I rarely ran out of ammo on RE2, RE3, or RECV. REmake is the only RE game I've played where you have to be conservative for most of the game and that's really mostly early on. I good way of conserving ammo is to learn how to dodge enemies. You only need to kill enemies that are going to cause problems for you later especially in REmake where you don't get a lot of ammo at the start.
As far as the old RE games being scary, only the first 2 were. RE3 was hardly scary other than a few jump scares from Nemesis. Most of the time you knew he was coming because the music would change or completely stop. I can't see how anybody can think RECV was scary. Super Mario World scared me more than that game.
The only time besides Jump scares the old games had where "Oh crap no more ammo" scares and to be honest it either ended in a massive Knife win or in the terms of fighting harder enimes "Dead I guess I have to reload moments." Really didn't add much IMO.
Currently playing:TES:V Skyrim, Fallout: New Vegas. Currently Waiting for: DBZ Budokai HD Collection, Fallout 4, GTAV, Naruto UNS3, and Dawnguard PS3, and RE6