Yes, you can try many of our apps for free. Most of our apps offer a trial period and can be installed through the Shopify App Store. When you install the app it will ask you to accept the charge, but if you look closely you'll notice the trial period is applied upfront.
If you've previously installed a specific app, you may not be provided with a trial period when you go to re-install. This is due to the way Shopify's billing system works.
However, please contact our Merchant Success team if this is the case, and we'll be glad to assist accordingly.