The UCSC Genome Browser offers several ways to obtain this information, depending on your requirements.
The Genome Browser downloads site provides prepackaged downloads of 1000 bp, 2000 bp, and 5000 bp upstream sequence for RefSeq genes that have a coding portion and annotated 5' and 3' UTRs. You can obtain these from the bigZips downloads directory for the assembly of interest.
To fetch the upstream sequence for a specific gene, use the Table Browser. Enter the genome, assembly, and select the knownGene table. Paste the gene name or accession number in the identifier field. Choose sequence for the output format type, then click the get output button. On the next page, select genomic. On the final page, you will have the opportunity to configure the amount of upstream promoter sequence to fetch, along with several other options. Click Get Sequence when you've finished configuring the output.
You can also use the Genome Browser to obtain sequence for a specific gene. Open the Genome Browser window to display the gene in which you're interested. Click the entry for the gene in the RefSeq or Known Genes track, then click the Genomic Sequence link. Alternatively, you can click the DNA link in the top menu bar of the Genome Browser tracks window to access options for displaying the sequence.