I think that Terraria has a bottom.
I'm not sure, because I've never reached it. I think I've got close, when the dirt has given way to ash before giving away to a vastness of nothing, but by that point I was being harried by fire imps and vertigo, and death was my next experience, not discovery.
There's another reason I'm sure. It's because Terraria is so full of stuff and things and all sorts that there's not really a reason to dig down that far. It's about your lateral movement rather than your vertical. It's about leaving whatever hovel you've created and heading out into the great beyond - because you know whatever you find, it's going to be interesting.
So I don't know that Terraria has a bottom, because I've been busy. I've been investigating meteor crashes. I've been exploring dungeons. I've been clearing away the corruption. I'll find that bottom, somewhere. I'll get round to it. But right now? Right now I'm having way too much fun in the places between here and there. Did I tell you about the time I stumbled upon an underground jungle? Good times, man, good times.
To grasp ineptly at the genre of nearest fit, Terraria is a 2D platformer. But it's also a building game, a farming simulator, an RPG and a co-op adventure game. It's been likened to Minecraft, but while they're both games that, at the fundamentals, are about digging blocks and building blocks, they're really not all that similar. The similarities are derived from the fact that they've both been massively popular.
Sure, you're digging, mining for ores and treasures that you can then use above ground to create magnificent constructions, but in Terraria that's just a starting point, somewhere to launch yourself off of, and into the rest of it all. There's not the depth of Minecraft here, the underlying sense of world and place, but that doesn't matter. You'll be far to distracted by every other thing to ever worry about that.
Above ground you've got the slimes. They're annoying but not really all that dangerous, unless you get swarmed. Then, as you dig down, the background will shift from brown dirt to darker brown dirt, and skeletons, giant worms and bats begin to appear. Deeper still, where the walls turn to ash and lava, you've got the fire imps, the bone serpents, the demons. And that's just when you head straight down.
Terraria has literal vertical difficulty. The further down you go, the more dangerous it gets. You can potter around in the first layer of the world all you want, but, in the tradition of the rogue-like, the deeper you go, the better the loot. Sure, you can hang out in the safe dirt layer, but you'll be stuck with copper ore, and you're unlikely to find any treasure chests. If you're going to range, might as well range far, right?
The world has spots of corruption all over the place that have their own monsters. Underground Jungles, Floating Islands, Dungeons, they've all got monsters that only show up when you enter their borders. Head in any one direction long enough, and you're going to find something that isn't a slime. And then you've got night, which brings the undead.
So no, you can't really potter around in just the one area. The further you get away from that safe spot where you've made your house, the more dangerous things are going to get, but, conversely, the better things will end up for you if you survive it. Each of these areas has unique items for you to find. Each with their own desirable effects. A breathing reed that lets you breathe underwater so long as the top of the reed is above the waterline. A cloud in a bottle that lets you double jump. A hook that you can strap to some chains to turn into a grapple.
I suppose, if you were properly scared of the outside world, you could just stay inside your house the whole time and knit, or something. Except sometimes you might get a Blood Moon at night, which lets zombies break down doors. Or the Goblin Army might attack, with their teleporting wizards that will come in and turn your knitting into ugly-smelling ash with a lightning bolt. Or hell, maybe a meteor will land on your house. Better to stay underground, where it's dangerous - just, y'know, less dangerous than up there.