A lot of systems that work this way also cap your fare so that you never pay more than the day rate. Say the day cap is £5, and an individual fare costs £2, then if you take two journeys you'll pay £2 each, but from the fifth journey on, you're capped and only pay £1. In some places, there's day and week caps, so if you travel every day of the week, the price will be capped again once you've travelled enough that week.
The Oyster system in London is a classic example of this - originally you needed to load money onto a separate card, now you can do it with your bank card instead, but it still all works the same. I believe it's also the cheapest option - the daily and weekly caps are cheaper than their paper ticket equivalents. You can probably get better deals in specific cases, but generally the Oyster system is the way to go. I know they're slowly bringing that concept in in other cities in the UK as well, and there are schemes around Europe that use an app with GPS as the "tap on, tap off" mechanism.