29 year son lives with me and has no income can I claim as a dependent?

[AmyW]

Yes, you may be able to claim your son as a Qualifying Relative dependent if:

• You provided more than half of his support.
• He made less than $4,050 in gross taxable income. (Social Security income generally doesn’t count here.)
• He lives with you (365 days in the year) or they are related to you.
• He isn't a dependent on someone else’s taxes.
• He isn't doing their taxes with a spouse (married filing jointly).
• He is a U.S. citizen, resident alien, national, or a Canadian or Mexican resident. 
• You can’t claim a dependent if you are a dependent on someone else’s taxes

You can view the rules for claiming a dependent on your tax return here. 

[Hal_Al]

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit