There were several tactics mentioned: Google Bowling, Tattling, Google Insulation, Copyright Takedown Notices, Copied Content and Denial of Service
Google Bowling: XYZ is dropped off the search engines because their competitor framed them for breaking Google's guidelines in an extreme manner. An example would be to create, overnight, a 1000% more links for a competitor (than they already have). The key would be to produce so many links at once that Google's spam trigger would have no choice but to catch it. There are various ways to increase the chances of this happening but I would rather not describe them - after all this is not a tutorial.
Tattling: Is XYZ (the competitor) doing well because they purchased links? If so, and it is something you can prove, then it is entirely within your right to tell Google using their spam report form.
But will this work? It is touch and go whether your complaint will actually do anything in the short term because Google often collects these complaints and then upgrades its algorithm (if possible) to clean out other offenders using the same techniques; a more efficient process. That said, as Matt Cutts said in this video about link buying Google is not above occasionally using manual methods to clean out spam so you might get lucky and see an immediate result.
Google Insulation: Is there negative press in the top 10 about your service? Perhaps you have a competitor that just won't budge out of a top position? In either case a Google Insulation strategy is designed to raise the rankings of other websites that positively discuss your company/services/products in order to oust competitors out of the top 10 rankings. In its raw concept I believe this tactic is ethical because it is smart competitive marketing and a great tactic for reputation management (a hot topic these days).
Copyright Takedown Notices: If a person desperately needed to drop a competitor out of a top position it could engage in a legal action that requires Google to drop the ranking for a period of time based on copyright infringement. The problem here, of course, is that this tactic exposes the perpetrator so that they can be sued by the offended company if the accusation is baseless. Here is where you can submit a copyright infringement notice to Google.
Copied Content: Due to the fallible nature of Google's algorithm it is possible to 'steal' away the traffic to a competitor's particular content (say an article just published) by publishing it on your own site IF your site is more entrenched than the competitor's.
You see if Google is presented with two websites which have the same content it will be forced to choose which site is the original creator. The website with the longer history and/or the highest reputation will often win out and the loser will often find their content ranks lower (if at all).
Denial of Service: This is the most evil and clearly illegal tactic for removing a competitor. Denial of service attacks (DoS) are conducted by sending a large number requests to a competitor's web server at one time. The result is the competitor's server will either be too jammed with requests to function properly or it will simply crash from the burden of so many requests - effectively taking the competitor's website offline. Evil indeed.
Note: I find many of the methods of damaging a competitor's rankings horrifically unethical. That said, I believe that understanding these tactics is important in order to identify their use if they are applied against you.