All antennas radiate energy in three dimensions. However, while the theoretical isotropic antenna radiates along the X, Y and Z axes equally, real antennas don't behave that way. Some antennas radiate energy in a symmetrical pattern, while others are asymmetrical in nature.
The diagrams here were originally presented in an article by Trevor Marshall that appeared on Byte.com, Antennas Enhance WLAN Security. They provide 2-D and 3-D representations of antennas commonly used for WLAN applications. The same general principles apply to point-to-point antennas.
The first diagram shows the 2-D and 3-D patterns for a typical dipole antenna. This antenna provides gain by radiating more energy along the X axis than the Z axis. This is more precisely shown in the 2-D diagrams, where the azimuth view shows the pattern as viewed from above, and the elevation pattern shows the pattern as viewed from the side. The gain of this antenna is approximately 2.1 dBi.
The second diagram represents the pattern of a biquad antenna. This system radiates very little energy along the Z axis, instead concentrating it in a single direction along the X axis. The gain of this antenna is 11.3 dBi. The biquad antenna is designed to provide directional coverage within a building, so its beam width is wide. For point-to-point applications, narrower beam widths are highly desirable because the goal is to focus energy on a specific, distant point. Thus, for Yagi and Parabolic antennas, the signal along the X axis would be longer and narrower.
Most antenna manufacturers provide 2-D representations of their antenna patterns, so it's good to get accustomed to reading them in that manner. However, software is available to convert those 2-D patterns to 3-D (see Antennavis 0.2 and NSMA Antenna Pattern Plotter for Windows).
An interesting tutorial on antennas can be found at the AeroComm Antenna Tutorial.