Spectral Database for Organic Compounds (SDBS)
SDBS includes six different types of spectra for organic compounds: electron impact mass spectrum (EI-MS), Fourier transform infrared spectrum (FT-IR), 1H nuclear magnetic resonance (NMR) spectrum, 13C NMR spectrum, laser Raman spectrum, and electron spin resonance (ESR) spectrum.

NIST Chemistry WebBook
NIST Chemistry WebBook contains data compiled by NIST under the Standard Reference Data Program. Besides providing thermochemical, thermophysical, and ion energetics data, NIST Chemistry Webbook also provides IR spectrum, THz IR spectrum, mass spectrum and UV/Vis spectrum.

Dictionary of Organic Compounds
Reference QD246 .D5 (9 volumes), look for references ending in (ir) or (nmr) Available online through ChemNetBase

Reaxys is a web-based search and retrieval system for chemical compounds, bibliographic data and chemical reactions. Combined data from three sources: The Beilstein Database, The Gmelin Database, and The Patent Chemistry Database.

ChemSpider is a free chemical structure database providing fast text and structure search access to over 28 million structures from hundreds of data sources, including open spectra data.

Hundreds of atlases and more specialized books are available in the library.
Try narrowing your search by type of spectra or application See finding spectra in the library for more help

The Aldrich Library are good general atlases of NMR and IR spectra: Aldrich Library of 13C and 1H FT NMR Spectra - abbreviated FT-NMR in Aldrich Catalog Reference QC462.85 .A44 Aldrich Library of FT-IR Spectra - abbreviated FT-IR in Aldrich Catalog Reference QD96 .I5 P66

If you can't locate a spectrum in any of the reference materials, you may need to locate the spectrum, or even simply spectroscopic data, from a literature search.
See the chemical literature page for help with this. SciFinder Scholar is the recommended database for this task.

SciFinder provides online access to Chemical Abstracts, other Chemical Abstract Services databases, MedLine, and chemical patents. SciFinder offers various search options including reference searching, structure searching, and reaction searching.