UPDATED FOR TAX YEAR 2019
No - You cannot claim your wife as a dependent. You should still file "married filing jointly" even if you wife has no income. You cannot file "single" if you were married.
Married Filing Jointly is usually better than filing separately. When you file a joint return are normally eligible for more credits (child tax credit, education credits, earned income credit, child and dependent care credit).
[Edited | 4/14/2020 | 7:33am PDT]
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"