I have a table that lists episodes of a TV show and I have a genre column. Google sees the words in that column as keywords and I suspect that it thinks you are keyword spamming seeing as you may have the same word repeated over and over. How can I overcome this? It seems using images would act the same as the alt text would be the same as the text it's replacing.
No, it does not ensure that your site will be slapped. It only means that with each repetition of the same keyword, it starts getting less importance. Why do you feel your site is being slapped? There might be other reasons too. For instance, a quick run on Majestic SEO, shows me that you have no backlinks (that pass link juice).
It's time to throw away those old dusty SEO books, Google and other search engines for many years now care little about keyword density. Google has been pushing 'user experience' for a few years now and one of those factors that is less a factor is keyword density. If it makes sense to repeat a column with the genre then you should proceed to do so... because user experience is the most important factor because good sites get good links, get repeat visitors and so on....
While this doesn't answer your question if using 'Drama' a hundred times on a page weakens your page it does and it doesn't which I'll explain... It's believed that Google now uses a cap on keywords so once you're reached that cap you are no longer rewarded, of course excessive repeating of the keyword may end up in a slap but again, this would require really excessive use. Google has come a long way and I've worked a game site before and have had no problem ranking pages that repeat the keyword adventure and action for example, imdb is a great example if you look at the top 250 page, they have things like the description, so my advice would be do what your visitors will enjoy. It may be helpful to have lite descriptions of each TV show to lower the density of the genre but again, this shouldn't be your focus - user experience beats all SEO via nature links.