There's no once-and-for-all answer, but this is what I would go with:
* 99p may fool less numerate customers into believing they are paying less than they are. A fair proportion of the general population are not numerate enough to add £1.99 and £1.99. If these are in your target market and you find that ethically OK, you may be profiting from that. [Edited to add: sum deliberately chosen from experience; coincidentally matches article data]
* "Random" prices such as 86p can give a psychological sense that you have cut off as much as you can (even if you really haven't), attracting savvy shoppers, as long as you have a reasonably trustworthy brand on this point.
* Pricing even a penny or two less than the competition will attract price sensitive customers, particularly online. A lot of the general population are indeed price sensitive and are able to compare prices thanks to the internet. This depends on whether your level of service is perceived as reasonably comparable/fungible.
* Round prices e.g. £100,000 can give a sense of luxury or quality - you are not discounting because you are providing a high value product. Discounting often undermines any perception of quality - it's plausible that you would make fewer sales at £99,999
* a few pence difference is a bigger hit on (much bigger percentage of) your retail profit margin than it is on the customer's pocket. Research shows inconclusive results, and if it's not costing you sales, you should probably not take off the pennies.
It's interesting to compare this to the neighbour thread about developer rates - I doubt there are many developers charging £49.99 per hour [Edited to add: it's not even possible to select that as an option!]