What kind of detergent should I use in cell culture laboratory for cleaning purposes?
I can't tell if you're asking about glassware or work surfaces (hoods, benches etc), but...

We use regular old dawn dish soap in my lab because what's more important than the soap you use to wash you're glassware is the water you use to rinse it.  We teach our undergrads the 3-rinse-rule.  After soaping, every item gets 3 rinses with normal tapwater (or until no more suds forms- whichever comes last) followed by 3 rinses with deionized water.  We have DI water on tap which makes things easier.  I remember rinsing some glassware with acetone or other solvents in organic chem lab, but you shouldn't need to do anything like that for TC.  

The same principle holds true for work surfaces.  After cleaning, decontaminate with 70% ethanol, 10% bleach, envirocide or any other BSL2 recommended cleaner.