Well, this is a hard question.
There are generally 3 fonts that are in some form or other always supported. These fonts are Adobe Times, Adobe Helvetica, and Adobe Courier. The problem is that while every system and foundry have a clone of these, they have different names. They are also not entirely the same, but have the same metrics. The windows trio: Arial, Times New Roman, and Courier New are the monotype clones of them. On linux these have been provided as bitmap fonts by adobe, and as outlines in form of the URW Nimbus {Sans, Roman, Mono} clones. The outlines however are not pretty on screen (they are on a printer) as they lack hinting.
The solution would be to go for a multichoice for websites. As microsoft has at some point made the "core fonts" available for redistribution, many unix/linux systems do have those fonts available. So go with them. The liberation fonts are straight clones of the MS/monotype fonts, so should go ok as alternatives with a similar experience. Then go for "Helvetica", "Times", and "Courier" before the sans/serif/mono choice that puts you in the user's hands.