The two core components that define a roguelike tend to be random generation and a special style of turn-based action. There's a lot of other attributes common between a lot of roguelikes, such as one-way dungeons where there are no stairs to go back up, but these aren't required to be a proper roguelike. Even one of the most common aspects, "final death" where death deletes your save, is not present in all roguelikes.
Random Generation in roguelikes is a completely different scale than most other games. Entire dungeons are randomly generated. Some roguelikes feature specific dungeons that might have the same layout, but the majority of the game's dungeons will be randomly created. Some times these have persistence, where revisiting the same floor will have the same layout. Other times, there is no persistence and even returning backwards yields completely new floors.
A common extension is that items are randomly generated, and randomly attributed. Instead of seeing a staff and knowing that it's a staff of lightning bolt, you might see it as an oak staff before identification. But when you start a new save, an oak staff might be for healing hands while the staff of lightning bolt is now a cherry staff.
The end result is that past experience in the game will help you in forming strategies in roguelikes, but it will be difficult to play through with the same strategies since you can't rely on everything being the same.
Turn-based Action is the other main component. When you take a turn, all other entities will also take their turn. Until you take your turn, nothing will change. It gives a lot of time for people to plan their strategies. The methods in which turns advance will very greatly between many roguelikes: ADOM has a complex speed/energy system for getting your next turn while POWDER has a simple 5-tier turn system for different variations of speed. But you'll always be able to breathe when it is your turn.
As InvaderSkoodge pointed out in his comment link to the origin of Rogue-likes
The roguelike genre takes its name from Rogue, a role-playing video game based on the Dungeons & Dragons role-playing games, including concepts such as stats and experience points.
Games that follow the Rogue trend will often include features such as:
- Randomized Dungeons
- Dungeons and Dragons based leveling
- Unforgiving difficulty (lack of a checkpoint system, perma-death, etc.)
Some good examples of rogue-likes, or games inspired by the roguelike genre, are FTL: Faster Than Light, Crawl, Brogue, Nethack, "Hack, Slash, Loot", and, obviously, Rogue.
Best Answer
A roguelite is not-quite-a-roguelike. It's a fuzzy definition, but it's a starting place. (I've also heard the term roguelikelike.)
Back in 2008, some guys at the International Roguelike Development Conference 2008 in Berlin were annoyed about how some games were claiming to be roguelikes, but they weren't enough like Rogue. So they nailed down a fairly-solid definition of what was allowed to call itself a "roguelike." Not everyone subscribes to this definition, but it's a definition, and so it gets used. Here are the "high-value" points that a game should have to be called a roguelike by the Berlin Interpretation:
There's also a half-dozen "low-value" factors that are often part of a roguelike, but aren't required. I'm ignoring these, because they don't help us find the line between a roguelike and a roguelite.
Not every formally-approved roguelike follows every one of those tenets: #5, "only one game mode", gets violated on a regular basis in small ways: Ancient Domains of Mystery (ADOM), Iter Vehemens Ad Necem (IVAN), and Alphaman each have an overland map of some sort. So even roguelikes aren't always roguelikes. (#5 should really get moved to the "low-value factors" section of the Berlin Interpretation, or modified to add "usually". And it really needs an exception for inventory management or some such, because a too-strict reading could exclude Rogue itself from being a roguelike!)
The line between roguelike an roguelite is fuzzy; it resembles the definition of pornography a bit: "I'll know it when I see it." (SFW) A roguelite is missing one or more of those high-value characteristics, but missing one or more of those traits doesn't automatically make it a roguelite. And it might be possible to make a game that hits all of the high-value characteristics and yet isn't a roguelike. Here's a few examples of roguelites:
There are also some alternate definitions of roguelike. I've used the Berlin Interpretation here because it's the most strongly-defined term, but even among people who create roguelikes, there's no consensus. Each of the definitions strongly resemble each other, but different people pick different traits to be "most important," and different traits that are "common among roguelikes, but not mandatory."
It's hard to nail down what a roguelite is because all you can really say is "See that? It's not that. But it's kinda close." There's a number of them now, and they all diverge from a classic roguelike in different ways.