The National Center for Biotechnology Information runs the most useful website for bioinformatics. There you will find GenBank (the national repository for DNA and protein sequences), the Blast servers for searching those databases, the PubMed database of biomedical literature, and much more.
Besides NCBI, the most useful sites for human genome sequence data are the Human Genome Browser (the University of California at Santa Cruz) and ENSEMBL (EBI-EMBL and the Sanger Centre).
The National Human Genome Research Institute has a variety of useful items, including links to all major sequencing centers. (Look under "Genomic and Genetic Resources".)
The International Society for Computational Biology has links to online courses and books, to training programs, etc.
The Pacific Symposium on Biocomputing has PDF versions of papers from the last five years.
The Sanger Center's website for Chr. 22 is definitely worth visiting.
RepeatMasker identifies and masks interspersed repeats (such as Alu and L1 elements) and low-complexity regions (such a dinucleotide repeat ACACACAC...).
GenScan is the best of many ab initio genefinders on the Web.
Genotator and NIX are two of several existing tools that integrate results from homology-based and ab initio genefinders.
PipMaker compares two genomic DNA sequences.
Pfam, BLOCKS, PRINTS and PROSITE search a sequence for regions that belong to certain families of domains.
ClustalW performs multiple sequence alignment.
Regulatory Sequence Analysis Tools perform computational analysis of yeast regulatory sequences.
MEME searches a set of protein or DNA sequences for motifs (short patterns) that occur in many of the sequences.
AlignACE source code can be downloaded and used to search of motifs in a set of DNA sequences, or the server can be used.
The Wadsworth Center provides the Gibbs Motif Sampler to search for motifs in a set of protein or DNA sequences.