Minecraft wiki entry for Up_to_Infdev_20100325, associated text: X/Z: 512 - Clouds stop rendering
X/Z: -512 / 1,024 - The sky box stops rendering.
X/Z: 2,048 - The first noticeable jitter begins, with the hitbox appearing to flicker slightly around blocks.
X/Z: 16,384 - First noticeable world rendering issue begins, with the borders of chunks beginning to become visible and the chunks appearing to shake slightly.
X/Z: 32,768 - The world rendering bug present in Infdev 624 through Beta 1.7.3 begins to manifest, with the hitbox being slightly offset from the blocks.
X/Z: 65,536 - Particles begin to lose precision, appearing more blocky and stretched.
X/Z: 131,072 - Hitbox outline begins to deform and shake visually.
X/Z: >1,048,576 - The world rendering fails when looking at certain angles, causing the screen to flicker. It becomes very noticeable beyond X/Z: 2,000,000.
X/Z: 16,777,216 - Blocks stop being solid, causing the player to fall into the void. However, the player can still swim through water.
X/Z: 268,435,456 - The gaps between chunks start to become multiple blocks long, making the world look like stripes on one axis and a grid pattern on both axis.
X/Z: 2,147,483,647 - The world stops generating terrain and the map appears blank from here on out with only the Sun and Moon.
X/Z: Infinity - The largest achievable distance Java can render(1.7976931348623157e+308, any numbers larger than that are simply referred as infinity on NaN). The sun and moon are gone and everything is blank with the default sky color.