You should be able to play pretty much anything with these specs. However, the Sempron CPU is surprisingly behind the times and mismatched to the RAM and GPU. So you'll definitely have some slowdown in more than a few games I'm afraid.
It really depends on how much a given game stresses the GPU vs. the CPU.
My Computer
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Custom-built
OS
Windows 7 Professional SP1 32-bit
CPU
Intel Core 2 Duo E6600 2.4GHz
Motherboard
Asus PL5D2
Memory
4GB DDR2-667 (4x1GB in dual-channel config)
Graphics Card(s)
nVidia GeForce 9800 GT
Sound Card
Creative X-Fi XtremeMusic
Monitor(s) Displays
Acer P236H
Screen Resolution
1920x1200 (DVI)
Hard Drives
OCZ SSD Vertex Plus 60GB SATA (Firmware 3.55), 64MB cache
Hitachi HD321KJ SATA, 320GB, 7200rpm, 16MB cache
You are lucky. It is an AM2 socket. There are many pretty good CPUs for around $50 that would fit - e.g. an AMD 5xxx+. Just check on the Wattage because the Sempron draws only 45 Watts. But the board may be able to do better.
My Computer
Computer Manufacturer/Model Number
HP, Dell, Gateway, Toshiba - 4 laptops and 2 desktops
I love how AMD keep sockets alive for such a long time!
With intel it seems to be a new socket per CPU family.
With amd you can have a 2-3 year old pc and still drop in a new CPU. Well apart from bulldozer lol.
Shame I'm such an intel slag
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My Computer
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Built by badgers!!!
OS
Windows 7 Ultimate x64, & Mac OS X 10.9.2
CPU
Intel Core i5 2500k
Motherboard
Asus P8z68 LE
Memory
Corsair Vengence 8gb 1866mhz
Graphics Card(s)
Nvidia GTX 770 OC
Monitor(s) Displays
2x ASUS LED 22" IPS
Screen Resolution
3840x1080
Hard Drives
240GB Crucial M500 SSD
120gb Corsair Force 3 SSD
1TB Western Digital
PSU
Corsair HX650w Modular
Case
Corsair Air 540
Cooling
Corsair H60 Push/Pull
Keyboard
Corsair K70/ Logitech G27 wheel
Mouse
Saitek R.A.T 9
Internet Speed
Too slow!
Other Info
AMD fusion E350N Home server-Windows Home Server 2011 (also made by badgers!)
2011 Macbook 2.4ghz Core2Duo, 4gb ddr3, 120gb Ocz Vertex SSD