Molecular drawing and graphics software
Avogadro - Molecular editing software. Great for getting energy minimised 3D representations that can be useful for predicting/rationalising reaction outcomes. Also good (pay attention students...) for getting accurate 3D structures to help you with problems and tutorial questions, as well as calculating distances between hydrogen atoms for NOE assignments.
UCSF Chimera - Good software for viewing 3D protein structures. Includes sequence alignment, surface predictions and can produce top quality structures for publication.
PyMOL - An alternative to UCSF Chimera. The educational version is free and in my personal experience I find them pretty comparable.
Autodock Vina - Allows ligand docking studies to be performed on crystal and NMR structures of proteins and peptides. This is the only docking software I have used but as a computer layman I found this very straight forward with plenty of online resources available for help.
Nuclear Magnetic Resonance (NMR) analysis
iNMR - The educational version of this software is free and has everything you need for analysing NMR spectra. The free version has a mildly annoying pop-up and shuts down every 30 minutes (just reopen it), but has most of the functions contained in the paid for version.
Chem 605 - Online resource for the Chemistry 605 course taught by Hans J. Reich at the University of Wisconsin. You can find notes on 1D- and 2D-NMR, as well as an excellent data bank of experimentally obtained chemical shifts (H-1, C-13, F-19, P-31, Se-77 and B-11), and a list of common NMR solvent impurities.
SDBS - The AIST spectral database for organic compounds. Contains H-1 NMR, C-13 NMR, EI-MS, FT-IR, laser Raman and ESR spectra of lots of organic compounds.
BMRB - The Biological Magnetic Resonance Data Bank is a data bank containing NMR data on proteins, peptides, nucleic acids and other biomolecules.
Mass spectrometry (MS) analysis
SIS Tools - Online resource that includes an exact mass calculator, isotope distribution calculator and MS spectra database.
Adduct calculator - Download the excel file, input your expected mass and get a big list of different possible adducts.
MassBank - Another spectral database.
Nucleic acid sequence tools
ExPASy Translate Tool - Translate DNA sequences into protein sequences.
Filter DNA - Removes non-DNA characters from downloaded gene sequences.
Reverse Complement - When you submit a plasmid for sequencing you should use both a forward (5' to 3') and reverse (3' to 5') primer. The sequencing results from the reverse primer must undergo a reverse compliment to read 5' to 3' (direction of protein translation). Simply copy your sequence data, paste into the text book and submit!
GenBank - NIH genetic sequence database.
BLAST - Compare your sequence data to all genetic sequences in GenBank or to specific DNA sequences of your choosing.
Clustal Omega - A multiple sequence alignment tool for DNA and protein sequences.
Protein and peptide tools
BLAST - You can also perform a BLAST search using protein sequences.
Reverse Translate - Tool for converting protein sequence to likely DNA sequence. Uses codon usage charts specific to individual strains (e.g. E. coli).
PeptideCutter - An online tool that identifies possible protease cleavage sites within a protein based on amino acid sequence (does not take tertiary structure into account).
ProtParam - A tool to calculate physical and chemical parameters of given protein (stored or user defined). This includes the molecular weight, theoretical pI, amino acids, atomic details, extinction coefficient and predicted stability.
RCSB PDB - A data bank of NMR derived and X-ray crystal derived protein structures.