Being an environmental scientist, I've spent years of my life living out of a tent in the field, and through extensive trial and error now have a pretty solid and stable repertoire in my pack. If you're new to backpacking and are planning a trip, here are my recommendations for reliable but affordable gear (just the basics!). These have all been field-tested by the pros (i.e. me and my field assistants :) ).
Click through after the break for many more gear recs!
As always, when planning a backpacking trip be sure you check the weather, tell someone where you're going (and ideally have some emergency contact method - I always use the Spot Tracker for any trips longer than a few days - or at least know that there will be cell service), bring lots of water and refill whenever you hit a water source, and triple-count the calories you're hiking in to make sure you've brought enough. It's also always good to check for unique safety risks to the areas you're hiking in (dangerous stream crossings, fire warnings/rules, bears, etc.).
And, of course, don't forget your Snuggie! Happy camping!