Short answer, no. Long answer...yes.
It all depends on your laptop really, specifically the mother bored. Most laptops have integrated graphics cards that can not be upgraded as they are part of the mother bored, which lacks the ports to plug in the new adapter not to mention the space. Some however do have dedicated graphics cards and these can be upgraded. The cards for laptop GPU's are more difficult to find and can be quite expensive. Also they do not offer the same kind of performance of there desktop counterparts, so don't expect top end graphics. Generally they at the most will be able to do medium setting on relatively new games. (Starcrft I, MW3,etc...)
Installing a new card into your laptop can be quite complicated as you have a lot hardware all packed into a small space, but it's not imposable and once again, depending on the mother bored your laptop has, may be a lot easier. It really varies system by system.
All in all it's probably not worth the time and money to upgrade, if you must it's possible and you may want to have a look at e-bay to see if there are any decently priced second hand cards out there, that may save you some money. Just type the name of the card into google followed by 'review' to get an idea of the performance.
**EDIT**
It would be helpful if you told us what type of laptop you have. The manufacture and the model would be ideal.