Why does El Niño only exist in the Pacific Ocean and not the Atlantic/Indian Oceans?
First, to describe El Niño as a Pacific Ocean event seems overly simplistic. The effects of El Niño are felt worldwide as can be seemed by a principal component (EOF) analysis (e.g., Alexander et al., 2002). Also, using the term "El Niño" to describe the entire oscillation (ENSO, El Niño Southern oscillation) can lead to confusions as the term "El Niño" corresponds to one of the phases of the oscillation.

The size of the Pacific Ocean and the lack of equatorial constraints makes it a prime candidate for large oceanic fluctuations such as ENSO. The large distance between the western and eastern sides of the basin allows for a more dynamic equilibrium with the presence of large scale waves (Kelvin and Rossby; e.g., Kirtman, 1997). This equilibrium can be altered by external (atmospheric) forcing resulting in the different modes of oscillation of ENSO.

Apart from that, there are a number of significant modes of oscillations (see http://www.esrl.noaa.gov/psd/data/climateindices/list/ for a very good list) that occur in basins outside the Pacific ocean. A good example is the North Atlantic Oscillation (NAO; Hurrel [1985, Science]; http://www.cpc.ncep.noaa.gov/products/precip/CWlink/pna/nao.shtml) that affects not only the North Atlantic but also the climate of Europe and North America.

Other examples of modes of climate variability include the Pacific Decadal Oscillation (PDO; Zhang et al., 1997), the Atlantic Multidecadal Oscillation (AMO; Schlesinger &amp; Ramankutty, 1994), or the Arctic Oscillation (AO; Thompson &amp; Wallace, 1998).