Co-founder of Grow or Die. Former Director of Growth at I Will Teach You To Be Rich and KISSmetrics.
Many well-known SaaS companies have doubled their prices. I've personally worked with a few that have gone through it. In most cases, your conversion rates stay the same and you see a huge jump in revenue.
This is because people tend to under-price themselves. Also, your product improves over time so it provides more value and can support a higher price.
But don't raise prices for old customers. Grandfather them in so their plans stay the same price. In the long run, it won't make a difference to your growth since most of them will churn out anyway.
If you raise prices on current customers, you'll get a huge backlash. It gets nasty. I'm pretty sure that Zendesk tried it and had to reverse the price increase.
I highly recommend raising your price by 100% for a month on new customers. Keep a close eye on your revenue and your conversion rates. If things don't go well, you can easily reverse it and discount everyone that paid for the more expensive plan. Either way, you'll know what your market will actually support.