Are there any taxes US companies/citizen has to pay if their software development projects are outsourced to India?
Generally, no. If you're a U.S. based company, you may outsource the development of your software development projects, or the creation of your intangible property. Payments made to non U.S. persons or companies that are performing the work outside of the U.S., should provide you a Form W-8BEN or W-8BEN-E to evidence their non U.S. tax status. If you don't collect this withholding certificate, you may be obligated to withholding taxes on the gross amount of payments submitted to the India company for their services.
Taxes are paid on income.
Your question seems related to cost of development, which is an expense.
So you'll write off expenses, not pay taxes on expenses.
Note: If you're a US citizen you'll pay tax on world wide income.
Tip: Better to always double check with your Tax Person about tax questions... as making long term business choices to optimize taxes... if done incorrectly... can be very costly...