Let's look at the primary foodstuffs used analogously to alcohol in MLP:
Salt:
Salt, or more accurately mineral salt licks, are implied to be something of a riff off drinking. There is no real reason to assume this causes motor or judgement inhibition and thus making it look like it inebriates a single character appears to be a one-off joke.
Sugar/Fat (dragons only):
Spike eating donuts is the only time we ever see him consuming fatty food or sugary food, so it could go either way.
The reason I bring this up is because it seems he does have some inebriation-like behavior. Dragons obviously have different physiology than ponies do, and since gemstones (mostly aluminum-silicate crystals like ruby and sapphire) taste 'delicious', then it would not be difficult to interpreting a dragon's reaction to complex carbohydrates in the same way [we] do to alcohol.
Cider:
Since the only time we ever see cider actually being consumed by characters is when it was made fresh, it's difficult to argue that this ciders is "hard" fermented cider. But the prominence of apple-based food and drink in the Apple family renders it quite possible that they also make hard cider kept for special occasions.
That said, I think they all have enough common sense to drink responsibly and sure-up before reaching their limits. In other words, I seriously doubt that any of the characters, considered according to their behaviors in the show's canon, would ever consume enough to become drunk outright. The characters who would probably skirt the limit and get buzzed might be Rainbow Dash, and maybe Rarity or Twilight if Rarity had somepony she wanted to impress or Twilight just wanted to experience and "research", though they definitely wouldn't be doing such a thing regularly. Applejack would have a good sense of moderation drilled into her by the Family, Fluttershy would have too strong a mental barrier and perhaps fear of inebriation to ever drink more than a very small amount, and Pinkie Pie would have enough party-sense to not overdo it. On that lattermost detail, the reason would be because out of any of the characters, Pinkie Pie probably has become drunk before, and knowing what it's like, intends not to do it again, for concern of ruining the party. I mean, she can get pretty off-the-handle with just fruit punch.