Echo Planar Imaging
Instead of measuring just one echo after each excitation pulse, it is possible to acquire many echoes. As long as the precessing magnetisation in the xy plane has not decayed away, it can be sampled (the frequency encoding gradient will need to be switched on, of course). Echo planar imaging (EPI) can the thought of as an "add on" to a pulse sequence, to acquire more signals from each excitation pulse. There are some disadvantages to EPI (see Further Reading list).

EPI readout added onto a conventional SE pulse sequence. In this example, five MRI signals are phase encoded and frequency encoded (and measured) after one excitation pulse. In this example, the image acquisition time is divided by five. An effective echo time is defined as the time to the echo which corresponds to the least phase encoding.
The first MRI signal acquired as seen in the figure above has the starting phase encoding gradient. Each subsequent echo which is acquired has this phase encoding slightly "undone" by a smaller phase encoding gradient in the opposite direction (blipped EPI). An effective echo time for in a sequence like this is defined as the time to the echo which has the least phase encoding.

The third echo in the figure above is the nearest to the centre of k-space (no phase encoding). The effective echo time is defined this echo (TEeff). The TEeff will change for different phase encoding schemes. The next time the SE-EPI pulse sequence is run, k-space lines adjacent to these are filled. (This is called segmenting k-space.)

GE-EPI, compared to GE, affords better resolution and smaller image acquisition times, but is more susceptible to signal loss from T2* effects (arrows). This is because they accumulate throughout the echo train. Note signal loss surrounding the cardiac vein and to the right of the left ventricle (anterolateral, down arrow) in the GE-EPI image.
Further reading on this topic:
Books: Q&A in MRI p262, MRI From Picture to Proton p319
Online: Medcyclopaedia