The easiest and arguably cheapest way to improve the zoom on your camera is to move yourself closer to the object you wish to embiggen. Alternatively, you could shell out for Canon's SX60, which features a 21-1365mm lens that offers 65x optical zoom. Yes, sixty-five times. How good is that exactly? Well, these videos should demonstrate the camera's abilities pretty well.
The first clip is from a YouTube user by the handle "VosGad". It starts with the camera fully zoomed on a full moon, revealing quite a bit of detail on the surface. About 20 seconds in, the camera zooms out and the moon becomes a tiny, unresolved yellow-white dot in the sky. The rest of the video has the camera zooming in and out and is otherwise unremarkable.
This next one is from the Canon's Swedish YouTube channel. Again, it's the Powershot SX60, though instead of the moon, it's a group of people standing on a hilltop. Nothing too extraordinary — until we zoom out and realise the photographer is positioned on the other side of a rather large lake.
While the SX60's does the heavy lifting, the 16.1-megapixel, 6.17 x 4.55mm CMOS probably helps also.