Ok so i've seen thousands of topics asking if they can run it. If you really want to know then there are a few things you can do:
1:
http://cyri.systemrequirementslab.com/CYRI/
Go to this website, find Starcraft 2 in the drop box and run the online program. This will tell you how well your PC will handle the game.
2: Use your brain
The minimum requirements are as follows:
PC Minimum System Requirements*:
Windows® XP/Windows Vista®/Windows® 7 (Updated with the latest Service Packs) with DirectX® 9.0c2.6 GHz Pentium® IV or equivalent AMD Athlon® processor128 MB PCIe NVIDIA® GeForce® 6600 GT or ATI Radeon® 9800 PRO video card or better12 GB available HD space1 GB RAM (1.5 GB required for Windows Vista®/Windows® 7 users)DVD-ROM driveBroadband Internet connection1024X720 minimum display resolution
PC Recommended Specifications:
Windows Vista®/Windows® 7Dual Core 2.4Ghz Processor2 GB RAM512 MB NVIDIA® GeForce® 8800 GTX or ATI Radeon® HD 3870 or better
Do your best to try and match your PC to these requirements. More RAM= better, More Video Card Ram= better
3: LEARN a little about your PC
Alot of people claim to not know much about their PC. For you i have composed this list:
VIDEO CARDS:
Here is a list of some video cards. Figure out what video card you have and match it to this list:
Nvidia

from best to worst)
GeForce GTX 480
GeForce GTX 470
GeForce GTX 465
GeForce GTX 460
GeForce GTX 295
GeForce GTX 285
GeForce GTX 285 for Mac
GeForce GTX 280
GeForce GTX 275
GeForce GTX 260
GeForce GTS 250
GeForce 9800 GX2
GeForce 9800 GTX+
GeForce 9800 GTX
GeForce 9800 GT
GeForce 8800 GT(Blizzard Recommended)
GeForce 8800 GTS
GeForce 7950 GX 2
GeForce 7950 GTX 2
GeForce 7950 GT
GeForce 7900 GTX
GeForce 7800 GTX
GeForce GT 240*
GeForce GT 220*
GeForce 210
GeForce 9600 GT*
GeForce 9600 GSO 512
GeForce 9600 GSO
GeForce 7900 GT*
GeForce 7900 GS
GeForce 7900 Go
GeForce 7800 GT*
GeForce 7800 Go
GeForce 7800 GS
GeForce 6800 Ultra
GeForce 6800 GT OC
GeForce 9500 GT
Geforce 8500 GT
Geforce 8600 GTS
Geforce 8600 GT
GeForce 7600 GT
GeForce 7600 GS
GeForce 6800 GT
GeForce 6800 GS
GeForce 6800
GeForce 6600 GT OC
GeForce 9400 GT
GeForce 8400 GS
GeForce 8300 GS
GeForce 7300 GT
GeForce 6800 LE
GeForce 6600 GT(minimum requirement)
ATI

from best to worst)
ATI Radeon™ HD 5970 Graphics
ATI Radeon™ HD 5870 Eyefinity 6 Edition Graphics
ATI Radeon™ HD 5870 Graphics
ATI Radeon™ HD 5850 Graphics
ATI Radeon™ HD 5830 Graphics
ATI Radeon™ HD 5770 Graphics
ATI Radeon™ HD 5750 Graphics
ATI Radeon™ HD 5670 Graphics
ATI Radeon™ HD 5570 Graphics
ATI Radeon™ HD 5550 Graphics
ATI Radeon™ HD 5450 Graphics
ATI Radeon™ HD 4870 X2 Graphics
ATI Radeon™ HD 4890 Graphics
ATI Radeon™ HD 4870 Graphics
ATI Radeon™ HD 4850 Graphics
ATI Radeon™ HD 4830 Graphics
ATI Radeon™ HD 4770 Graphics
ATI Radeon™ HD 4600 Series
ATI Radeon™ HD 4550 Graphics
ATI Radeon™ HD 4300 Series
ATI Radeon™ HD 4200 Series
Radeon HD 3870 X2
Radeon HD 3870(Blizzard Recommended)
Radeon HD 3850
Radeon HD 2900 XT
Radeon HD 2900 GT
Radeon HD 2900 Pro
Radeon X1950 PRO
Radeon X1950 XTX
Radeon X1950 XT
Radeon X1950 GT
Radeon X1900 GT
Radeon X1900 XTX
Radeon X1900 XT
Radeon X1900 PRO
Radeon X1900 AIW
Radeon X800XT
Radeon X800XT AIW
Radeon X800 Pro
Radeon X800XL
Radeon X800GTO
Radeon X850XT PE
Radeon X850XT
Radeon X1650 XT
Radeon X1650 Pro
Radeon X1800XT
Radeon X1800XL AIW
Radeon X1800XL
Radeon X1800 GTO
Mobility Radeon HD 2700
Mobility Radeon HD 3600
Radeon HD 2600 X2
Radeon X700XT
Radeon X700 Pro
Radeon X1550
Radeon X1600 Pro
Radeon X1600XT
Mobility Radeon HD 2600
Mobility Radeon HD 2600 XT
Mobility Radeon HD 3400
Radeon HD 2600
Radeon HD 3650
Radeon 9800 Pro(Blizzard Minimum Requirement)
If your card is below minimum you cannot play the game. If your card is minimum you will be playing on LOW settings with noticable framerate lag. If you are between the minimum and recommended you will be playing between LOW and MEDIUM settings. If you meet the Recommended then you will be playing on MEDIUM or HIGH settings. If you slightly exceed the Recommended you will be playing on High to Ultra. If you have an Nvidia GTX 200 or more , or a Radeon 4000 series or more, you will be playing this game on ULTRA.
CPU's:
The minimum requirement is a2.6 GHz Pentium® IV orAMD Athlon® processo
As long as you are above this it wont effect performance too much.
FINAL WORDS
If you are still un-sure of your computer OR have something to add to this topic as it is probably not perfect, feel free to ask away or leave an addition to my post. It would also be good if a sticky was requested for this.