Which Software Can Open .eps and .ai Files?

EPS and files can be opened or imported with following applications (to name just a few)...

Vector editors like:
Adobe Illustrator
Corel Draw
Xara Xtreme
Inkscape

Raster image editors like:
Adobe Photoshop
Corel PhotoPaint
GIMP

Desktop publishing apps like:
Adobe InDesign
Quark Xpress

3D software like:
3D Studio Max
Cinema 4D
Swift 3D

Office Apps like:
Microsoft Office
Open Office

AI is native Adobe illustrator format and can be opened or imported by majority of applications from Adobe Systems Incorporated and majority of 3D applications and raster image editors.

What Are The Most Common Vector Formats?

Most common vector formats are .eps, .ai, .svg and .wmf. EPS is most commonly used vector format and it can be opened with variety of popular applications. Majority of files on Vectorportal are in .ai and .eps format.

What Is Vector Graphics?

Vector graphics use geometrical formulas to represent images. Vector images have many advantages over raster images. Vector is resolution independent meaning you can resize 100x100 pixel image to 100x100 inches image without any loss of quality. That is not possible with raster images. In addition, images stored as vectors look better on devices (monitors and printers) with higher resolution, whereas raster images always appear the same regardless of a device's resolution. Another advantage of vector graphics is that representations of images often require less memory than raster images do.

More on vector vs. raster graphics on following links:

SignIndustry: Vector vs. Raster Graphics
Wikipedia: Vector graphics