You can use your iClicker in multiple classes: there's no need to buy one for each class. However, there are a couple scenarios in which you'd need to buy a new iClicker remote for one of your classes:
If you have an original iClicker or iClicker+, but your instructor requires iClicker 2.
All of our remotes will work alongside each other, but if your instructor will be asking numeric or alphanumeric questions, or using self-paced polling, you'll need an iClicker 2 to fully participate. The original iClicker and iClicker + have exactly the same functionality and there would never be a reason to purchase an iClicker + if you already have the original remote.
If you purchased iClicker GO, but your instructor requires a physical iClicker remote.
Your instructor will usually specify on his/her syllabus which iClicker remote is required. Check there before sending him/her an email. If you know you'll need to use iClicker in multiple classes, the iClicker 2 is the safest bet, since it will work no matter which question types your instructor requires.