Every non-native speaker of English should have a good grammar book and a good English-English dictionary for reference. Here are some useful print and online resources for non-native speakers.
Understanding and Using English Grammar, by Betty Azar. A comprehensive grammar reference that includes interactive language-learning activities. Available with workbook.
Longman Grammar of Spoken and Written English, by Douglas Biber et al. A reference grammar that reveals which structures, tenses, and lexical choices occur, and how their distribution differs in different types of texts.
Longman Dictionary of American English: Your Complete Guide to American English. Available with CD-ROM. Includes simple explanations and usage examples of idioms, along with exercises that will help with many troublespots.
Longman Dictionary of Contemporary English. Includes clear definitions and comprehensive coverage of spoken language. Words used frequently are marked as such.
Insights 1 & 2: A Content-based Approach to Academic Preparation, by Donna Briton et al. Includes readings and tapes of university lectures from across the curriculum, as well as discussion and writing topics intended to help college students synthesize information.