The PlayStation 1 had a copy protection system that measured physical properties of the disc which couldn't be replicated by normal CD writers. There were a few ways to get around this, but to be able to put a burned CD into your console and boot directly from it into the game (as usual) required the installation of a fairly complex mod chip. A lot of people alternatively used the "swap trick", which is how I used to play my imported original games.

The DreamCast's copy protection was heavily reliant on using dual-layer GD-ROM discs rather than regular CDs, even though they look the same to the naked eye. There were other checks in place as well, but simply using GD-ROMs was pretty effective in and of itself.

Unfortunately, Sega also added support for a thing called "MIL-CD" to the DreamCast. MIL-CD was intended to allow regular music CDs to include interactive multimedia components when played on the console. However, MIL-CD was supported for otherwise completely standard CDs, including burned CDs, and had no copy protection, because Sega wanted to make it as easy as possible for other companies to make MIL-CDs, so the format could spread and hopefully become popular. Someone found a way to "break out" of the MIL-CD system and take over the console to run arbitrary code like a regular, officially released game, and that was the end of DreamCast's copy protection. People couldn't just copy an original game disc 1:1 and have it work; some work had to be done on the game to put it on a burned CD and still have it run (sometimes quite a lot of work, actually), but no console modification was needed. Anyone with a DreamCast relased before Sega patched this issue (which seems to be most of them) can simply burn a CD and play it on their console, provided they can get a cracked copy of the game.

For the DC? yeah, it would play burned CDs no problem.

For the playstation? not sure. I had mine modded so I could import games from Japan but I don't believe it could play burned CDs.

Xbox and the 360 were easy to mod though and you could play burned games on those also.

But yeah the Dreamcast just did it right out of the box. no mods required.