http://www.taxibudapest.eu/
I emailed Tom at the above URL to pick us up at the main train station in Budapest. He responded quickly (always within 2-4 hours) and was waiting for us with our names on a sign.
The one-way fare from the train station to the Hilton Castle Hill was 15 Euros. The round trip fare was only 19 Euros total. Since we were switching hotels and would be leaving from the Hilton WestEnd, I had not booked the round trip. However, Tom said that it was no problem to get the 19-Euro fare and that he would pick us up at the other Hilton.
Tom prefers payment in Euros or U.S. dollars. The prices are clearly indicated on his web site. I paid in Euros because the current exchange rate is much more favorable.
Here is the best part. Upon dropping us off at the first hotel, I asked how much I should pay. "Nothing," Tom responded. "You pay the entire amount when I pick you up at the other hotel."
Later I emailed Tom again to ask him to move us from one Hilton to the other. Again, he responded promptly, was on time to meet us, and quoted me 9 Euros for this trip. I now owe Tom 28 Euros altogether. "Should I pay you something now?" Again, Tom said, "No, you pay when I pick you up to take you to the train station."
In addition to being prompt, Tom is polite and speaks decent English. I definitely recommend him if you need transportation in Budapest.