Textbooks:

Main course text

Model Theory: An Introduction by David Marker (Springer, 2002) (errata & corrigenda)
[used copies at the Coop; on reserve]

General texts

Saturated Model Theory by Gerald E. Sacks (W. A. Benjamin, 1972)

A Shorter Model Theory by Wilfrid Hodges (Cambridge, 1997) (errata & corrigenda)
[on reserve]

The Mathematics of Logic by Richard Kaye (Cambridge, 2007)
[on reserve]

A Course in Model Theory by Bruno Poizat (Springer, 2000)
[on reserve]

Model Theory by C. C. Chang and H. Jerome Keisler (3rd ed., North Holland, 1990)

Model Theory by Wilfrid Hodges (Cambridge, 1993)
[on reserve]

Survey articles:

Model Theory by Anand Pillay (AMS Notices, 2000)

Introduction to Model Theory by David Marker (MSRI)

First-order Model Theory by Wilfrid Hodges (SEP, 2005)

Infinitary logic and admissible sets

Barwise: Infinitary Logic and Admissible Sets by H. Jerome Keisler and Julia F. Knight (BSL, 2004)

Infinitary Logic by John L. Bell (SEP, 2006)

Applications to algebra and algebraic geometry

Model Theory, Algebra and Geometry by Deirdre Haskell, Anand Pillay, and Charles Steinhorn (MSRI/Cambridge, 2000)
[online]

Nonstandard models of arithmetic

Tennenbaum's Theorem by Richard Kaye

Nonstandard analysis

Chapter 12 of The Mathematics of Logic by Richard Kaye (see above)

Non-measurable sets via nonstandard analysis by Terry Tao (blog, 2008)

Nonstandard probability by S. Michael Webb (NDJFL, 1975)

Quantifier elimination algorithms

A Survey of Quantifier Elimination: Syntactic and Semantic Approaches by Ting Zhang

QEPCAD: Quantifier Elimination by Partial Cylindrical Algebraic Decomposition

Decidable rings and Hilbert's 10th Problem

Hilbert's Tenth Problem over rings of number-theoretic interest by Bjorn Poonen (AWS, 2003)

Undecidability in number theory by Bjorn Poonen (AMS Notices, 2008)

Computable Model Theory

Pure Computable Model Theory by Valentina Harizanov (Handbook of Recursive Mathematics, 1998)