The MOBI reader on the EZ Reader's (Hanlin V3 and V5) support italic and bold fonts.
All the mobile Adobe Digital Editions ports seem to use the standard Adobe provided fonts as their default, and these use fake italic and bold. However, it is in principle possible to replace the default fonts with ones that do include full italic and bold support. On the Opus and the EZ Reader's, this can only be done by editing the CSS of each ePub file individually, but there is now a hack for the Sony PRS-505 that allows the user to specify their own default fonts for all ePubs (
Replace DEFAULT epub fonts! (PRS-505)). A similar capability has been requested from the vendors of the Hanlin and PocketBook devices. Note that some ePubs will have embedded fonts, which are not changeable by the user.