I typically get a little more anxious than "baseline" when planning a long XC. Local, not really anymore. A quick weather check, my usual pre-flight routine, and let's go.
For XC's, the added tiny bit of anxiousness typically just keeps me focused on the routine... weather, good pre-flight, etc. Mainly weather. Stuff changes the further afield you fly. That's a given. You just hunt around and make sure you have "outs" and are ready to execute them.
When I first started flying, when I would start messing up landings or whatever... my shoulders would head for my ears. All tense.
My first CFI noticed it and karate-chopped me one day between the shoulder and neck and pointed it out... we both laughed.
Ever since then, when I feel my shoulders rising for something that's bugging me in flight, I make a mental effort to both figure out what it is, and also to forcibly relax my shoulders. Doesn't happen too often anymore, but when it does, it's a sign something's subconsciously bothering me about the flight, or I'm struggling with something.
Interestingly the most anxious I've felt in a long while was walking out to the airplane with Jesse our first night in Nebraska on the second flight seeing the fog covering the airport. My "VFR brain" was saying, "That's not something we're supposed to fly in, dude..." but we'd done a very thorough look at the weather, the Skew-T, etc etc etc... and had our "outs", etc.
Of course, anyone who followed along on those posts also knows that turned into my first IFR approach to minimums... and by minimums I mean we had to make sure we had the required items to descend past DA... it was low. Great experience.
The other voice in my head was going, "You don't know this CFII from Adam... you showed up here in Nebraska about three hours ago to fly with this guy you've never met before from an Internet website..."
There were two things that kept me walking out to that airplane... Jesse is a solid professional with a very calm and with no other good way to put it... "normal" demeanor, and Spike had offered up a personal comment to me prior to leaving Denver that Jesse knew his stuff.
I've climbed into a number of airplanes with really **** poor pilots and regretted it later. Luckily none have killed me or bent any airplanes, but my "this guy doesn't know what he's doing" meter is finely tuned. The meter never left the bottom peg with Jesse.
The other time the anxiety went up a bit, just enough to make me stop and think, was when Jesse and I had that temporary static system problem at night during taxi out. The safety training and what-not kicked in, and we both said simultaneously that we were going to taxi in and give it a closer look.
That unfortunately didn't alleviate all of our concerns, but we knew it looked like it was working properly on Alternate Static, so then the professionalism and thought process steps up a notch, and we pretty instinctively briefed the takeoff "a little harder" than usual...
"If the A/S seems wrong at any point during the takeoff you can either abort or ignore it completely and let the aircraft fly off when it's ready. Climb at a known angle and power setting for this aircraft until we're high enough to safely spend time troubleshooting again. We will not be going under the hood for the short trip to Lincoln, this will be all eyeballs outside VFR."
In short, replace the anxiety with a plan. The plan can change, but get it said out-loud and confirm everybody's "okay" with the plan. If there's no other pilot aboard, make sure you're "okay" with the plan. I talk to myself in those scenarios, others may handle it differently.
"Okay, wind picked up and this is going to be a pretty significant cross-wind landing... you know you're okay to do the landing but you've always had a tendency to relax control pressure at touchdown. Put the flight controls all the way into the wind at touch-down or as soon as possible thereafter. You know how to do this... checklist, GUMPS, flaaaaare... look up (my reminder to myself to look at the far end of the runway), okay full right aileron, elevator all the way back..."
I'd offer up the thought that the "anxiety" never goes away completely with each flight, beginning to end, but it lessens a lot over time, and gets more tuned-in to when things are really going sideways. Any time it has popped up and I've ignored it, I've kicked myself later on. Complacency.
If you're anxious... there's probably a reason. You find information, a problem, or whatever is causing it and act on it until the anxiety goes away. Similar vein to my post to the person who asked if they should fly a cheap local beater airplane... if you're not comfortable launching in it, then don't.
Part of the early anxiety is just knowing you don't have enough experience, and you have to suck it up and go get some.