Occasionally, people tell me they have actually said "LOL" instead of laughing (and then felt very stupid), but I don't think the internet has changed things very much. Within the internet, many practices from internet relay chat -- particularly abbreviations -- are being used on message boards a lot (where they are not really necessary), but I've never seen them, for example, in newspaper articles.
Apart from that, the internet has given us a few new words -- "spam" for "junk mail", for example, although most people still seem to differentiate between e-mail spam and the junk mail printed on paper.
So many things to say, so little time!
This question depends on one's mastery of English (if we're sticking only to English, I have no clue how it affects other languages) before the Internet comes into question. Adults who can competently speak and write English will have fun perhaps, and no problems, switching between the "spokenlized" (thanks, gxiang) version and proper English. However, if, let's say, a teenager, who has yet to completely understand proper English, is immersed too deeply into the crude and ever-changing forms of instange messages, email, etc., they may not be able to differentiate between correct and incorrect English.
This question begs to be focused on age, but it probably relies on a mastery of the language first, with maybe a tendency for youth to have more of this problem because they haven't had the years of practice an adult should have had since they are, by definition, older.