Off the top of my head, taxi services lack:

• Convenient hailing. A phone call works okay if you're home, where there isn't much noise and you speak the local language, but a web form is often much easier and less error-prone in other situations.
• Efficient coverage. Many areas either have sparse taxi coverage, or multiple taxi companies competing in an area, and if the one you call doesn't have enough drivers available and nearby, you're stuck waiting unreasonably long even if there are other ride options with better availability.
• Up-front journey-specific prices. We now have the technology to see what the total cost will be before we commit to a ride. We should be using it.
• A single point of hailing, where I can submit my location and destination, and be presented with my ride options from all the available providers.
• Accurate pick-up and drop-off time estimates. Even better with real-time taxi location.
• Quick arrival.
• Automated ride-sharing coordination among strangers.
• Fuel efficiency incentives. Most taxis I've taken have been heavy vehicles that guzzle petrol, passing the expense on to the environment and the customer.

I think most (maybe all) of this could be solved by something like a clearinghouse for taxi rides, effectively federating the various taxi services in an area, with a web app available for hailing.