I could be wrong and I probably am but I always figured that airlines have commitments toward certain companies that provide engines or aircraft. I know Northwest's DC-9's, A319/A320/A333, B752/B753, and B742/B744 all use Pratt & Whitney engines.
Almost right. Northwest uses the CFM56 engines on their 319s and 320s, which is a partnership of GE and SNECMA. The other option on the 320 series is the IAE V2500, which is a partnership of five companies including Rolls-Royce and Pratt & Whitney. Northwest is generally loyal to Pratt, so I'm not sure why they decided to go with CFM in that case. United, who is also a Pratt loyalist, chose IAE for their 319s and 320s.
Airbus and Boeing generally offer at least two choices of engines on their planes. The exceptions on the market today are the A340-500/600, which are only available with Rolls-Royce, the 777-200LR/300ER, which are only available with GE, and the 737-600/700/800/900ER, which are only available with CFM.