Several techniques can help you massage BLAST statistics to either hide significant alignments or make meaningless alignments appear highly significant. Why would you want to do this? If you have to ask, you're not the intended audience. Dishonest evil doers read on.
The easiest method to adjust the significance of all scores is to set the effective size of the search space either higher or lower. Command-line parameters in both NCBI-BLAST (-Y) and WU-BLAST (Y and Z) are available. You can also alter the scoring scheme by editing the scoring matrices. A more involved approach involves hacking the source code to set your own values for l, k, and H. WU-BLAST makes it all too easy because you can alter scores or set Karlin-Altschul parameters on the command line. Whatever approach you take, you will, of course, want to edit the footer to cover your tracks. The easiest way to do this is to run the search twice and diff the footers to determine what needs fixing.
With low gap penalties, you can make alignments between just about anything. For BLASTN, NCBI-BLAST always uses ungapped statistics, so you don't have to do much work to lie. Just hope that nobody notices all the gaps. This works best if you have a supervisor who is either too busy to look at alignments or wouldn't know a decent alignment if it bit him. NCBI-BLAST is very restrictive about what gap penalties you can employ for the protein-based BLAST programs. Your only choice here is to hack and recompile. WU-BLAST is very easy; set your gap costs low and include warnings on the command line to suppress messages about ungapped statistics.
Another way to trick the unobservant is to remove complexity filters. This works especially well when claiming that some anonymous low-complexity region or transcript is a cool gene. You can almost always find a small ORF that has a poor match to something with an interesting definition line. A poor match is only poor if you don't know how to fix the statistics. This approach even works when fooling scientific journals. (It really does. We've seen it happen.)