That completely depends on what games you want to play. You have a decent setup, so you should be able to play atleast some games. The biggest hurdle you'll run into is your graphics card. You have a GeForce 9300M. Those are rated at 64-Bit and only 256MB of ram. That's the low end of requirements on most of the newest high quality games. This basically means that you'll bearly be able to play the newer games like AC II and others.
The way you can tell whether or not you'll be able to play a game is to look up it's system requirements. The system requirements are usually shown on the box, or somewhere on the webpage that you're purchasing the game from. If you can't find the system requirements there, you can always look them up online.
For example, if you wanted to play Assassin's Creed II, you'd need to look up it's requirements.
Go to Google, Type in Assassin's Creed II System Requirements
You'll see a bunch of results, the easiest and most informative page is either the manufacturer's page or the wikipedia entry. Assassin's Creed II - Wikipedia, the free encyclopedia
We see here that Assassin's Creed II has two sets, one is Required (Absolute Minimum) one is Recommended. The required section is what you need to play the game at all, the recommend section is what the manufacturer recommends for an actual enjoyable gaming experience. In other words, if you have the required, but no recommended, you'll be able to play the game, but it may be choppy and or not as enjoyable as it should be.
AC II Requirements:
CPU: Core2Duo 1.8 or X2 2.4Ghz
Memory: 1.5GB for XP, 2GB for Vista/7
HD Space: 8GB
GFX Card: 256MB DirectX 9, Shader 3.0
Sound Card: DirectX 9.0
Internet: Constant High Speed Internet Connection (128Kbps Upstream +)
Recommended: (All of required attributes, plus...)
Core2Duo 2.6Ghz / Athlon 64 X2 6000+
GeForce 8800 GT / Radeon HD 4700
5.1 Channel Sound
Those requirements basically tell you that you have the required set but not the recommended. You processor is not quite as powerful as a 64 X2 6000+, your graphics card isn't up to par w/ a 8800 GT and you don't have 5.1 Channel Sound.
If you're confused when it comes to the graphics card, I don't blame you. NVIDIA's laptop series of graphics cards are a bit less powerful than the desktop numerical equivalent. In other words, a laptop needs a 9800M GT to equate to a 8800 GT in a desktop. You have a 9300M, so you have the equivalent of about a 8300 in a desktop.