Is it possible to use bold, italicised, and underlined text in skype IM (to the point where the person you're talking with can see the bold etc.)
No. Unfortunately it's not possible to markup IM text at this time.
It's actually been disabled recently. There were some abuses of HTML and Skype decided to turn off it's availability. There's been no word on when, if ever, it will be re-enabled.
It was removed but you can add color and bold, italics and underline to you're status by downloading the skype rich mood editor. It'd be great if they added something that'd let you do things to messages in skype, then I could type giant letters to my mates and put the important part in bold.
It is possible to send something in bold (by typing * before and after the word or whatever you have written, ex. how are *you* ) and italics (by typing _ , ex how are _you_ )