Roguelike game has some essential features which makes it a roguelike.
1. Permadeath. What would a roguelike be without YASD? Not a roguelike.
2. Random game world. This one is a bit more complex, because you can't have 100% random content. It's against the laws of physics. However the structure of levels is often random in the limits of the rules that define the layout of the level. It's safe to say that even as low as 50% random amount counts as a roguelike and that there must be some kind of generator routine that creates some of levels on the fly (key levels can be static).
3. Turn-based and tile-based. These two are one feature, because they create the tactical topology of a roguelike gameplay. Tiles can be ascii or graphics, it makes no difference. Traditionally ascii was used, because display adapters at that time had no graphics support.
4. Role-playing. This one is controversial, because no one knows exactly what computer role-playing is. Good thing is that we have a long history of role-playing in computer game form. Games like Ultima-series and also games based on D&D role-playing system has helped us to build a firm role-playing experience. Role-playing can be limited or complex, but more character classes, items, monsters, etc. is better. Games like Nethack and ADOM are both fine examples of roguelikes with qualified amount of role-playing.