The best replacement for multiple regression is anova.

The best alternatives to multiple regression are rated as following:
★★★★★  anova
★★★★  linear regression
★★★★  logistic regression
★★★  multivariate regression
★★  simple regression
★★  ancova
★  general linear model
★  sem
★  stepwise regression
★  simple linear regression
★  hierarchical regression
★  regression
★  factor analysis
  manova
  partial correlation
  multivariate analysis
  structural equation modeling
  correlation analysis
  simple
  path analysis
  single regression
  nonlinear regression
  multiple correlation

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Speaking about multiple regression, one probably shouldn't forget about dummy variables.

Other search terms related to multiple regression and their ratings are:
★★★★★ dummy variables
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multiple regression
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