Will I regret paying cash for a house?

After almost a decade of saving and budgeting, I will have saved about 650k. I'm ready to buy a house and I'm unsure if I should put the money into a house or put a small amount down and invest my money elsewhere.<br><br>I currently live in a 3 bedroom apartment that is 1600 sqft. It's a bit cramped, but I don't need a lot of space. The house I'm looking at is in a nice neighborhood and it's a 4 bedroom 2500 sqft house with a decent size backyard. The price range for this house is 620k. <br><br>I have a 401k that I contribute 15% of my paycheck each month and my company matches an additional 5%. I also have an IRA and put away 1k/month. My retirement savings total about 120k currently. <br><br>I make about 250k per year and my expenses are very low, not including rent. I drive a 2015 car and save for everything. <br><br>I don't want to ever have a mortgage, but I also don't want to miss an opportunity to make money on my money. I'm not very good with numbers so I thought I'd throw it out on here with the hope that someone can help me out.