The Dark Horse Analytics blog has the best explanation on how to make tables more visually appealing by actually removing the distracting visual elements from them:
If you look at the blog you'll see that they advise against the 'zebra stripes' approach, which in my experience causes other design problems due to the alternating nature of colours. You should be able to convert any alternate colour row tables to ones without using them if you think more carefully about the use of styling in your tables. It actually makes the design more flexible and adaptable.
Just to provide a balanced argument, here is another article that does some testing on different strategies for table designs:
The only issue I have with this article is that it doesn't compare plain table styling to the optimized table styling like what the Darkhorse Analytics people suggested, so you can't really compare the results.