Going the opposite way on each side seems to be symmetric.
But, Sheldon Brown disagrees;

Whether you start from the middle or from the ends, make sure to go in the same direction on both sides. I generally start from the underside of the bar, with the tape feeding outwards. You can do it the other way too, but make sure you follow the same pattern on both sides.

What sayeth you?

i think he meant go up or down on both sides, not up one side and down the other

I find that starting at the middle and going down makes the tape more likely to curl up along the edges with use. Sliding your hands down the bars, you catch on those edges.

You want mirror symmentry, not side by side symmetry.

Fat bar tape (Cinelli Cork etc.) Bottom->top, reason: see TampaRaleighs post
thin bar tape like Benotto: top->bottom, reason: clean end with the provided colour-matched plug

This.

Though I did a Top to Bottom wrap last time and as martl said, definitely cleaner. It will need replacing soon though because of the issues mentioned by TampaRaleigh.

if you pull the tape tight when installing it doesn't curl as much

I agree with Martl. Back when I used cotton tape or plastic like Benotto, you would start at the top and stuff the cut end inside the bars. With fatter bar tapes starting with Bike Ribbon for me, start at the bottom. I usually wrap so that the tape is coming from the underside of the bar and wrapping around to the outside. Grip pressure will tend to tighten it this way.

Works for me. I always wrapped the old thin plastic stuff top-to-bottom and the thicker self-adhesive cloth tape bottom-to-top, starting clockwise on the right and anticlockwise on the left, so that the final wrap would be forward over the top of the bar.

I did Capo #1 in sprint tape, i.e., from the bottom to the brake handle only, and it looks very period-correct. In fact, the 1962 Capo catalog depicts this treatment.

Of course he did!

I sometimes do that relative to the brake levers. With Cinelli (original design bar caps) I start at the bar end and work up to the lever, one approx 70 mm section behind the lever and then from the central zone of the bar to the lever. No sticky tape required to terminate. Downside is that the upper regions at the bend can creep.

Vinyl tape is center to the end.

Modern tape ("Cinelli padded") is end to center. Finishing tape required, I taper the end as to keep the sticky tape band as narrow as possible.

This is true if you ride on the tops or hoods, but if you spend more time in the drops, then wrapping top-down actually helps to prevent the edges from curling.

Bottom up, towards the middle. That means counter clockwise on the right side, clockwise on the left.

Start at ends and wrap towards the stem.

This has been my experience as well. I also install cotton tape wet as it seems to give it more stretch when wrapping. Let the tape dry overnight and it shrinks tight to the bar, no rolling edges anywhere even after a full season of use.

This is what I was looking for, and makes sense as I picture the "mirror symmetry" mentioned earlier.

It seems like the Sheldon Brown directions suggest going counter-clockwise on both sides...

Going from the ends to the middle is a given with cork tape.

Do you mean you feed the tape inwards as you wrap? Wouldn't that tend to loosen the tape as you grip the bars in the drops?

I wrap bar end to stem, feeding the tape outwards as I wrap.

Still struggling with bottom to top or top to bottom. Way back in the 70's it was always top to bottom using the plugs to end the tape. I was surprized a few years ago (<10) to see bottom to top. When I bought my 84 Colnago, it still had the Bennotto tape and was wrapped bottom to top.

I think that's mainly because cloth/thinner tape was the norm back then, so it was easy to tuck it under the bar end plugs. With cork/thicker tape, it can still be tucked in, but it's trickier and usually easier to just terminate it with tape at the top.

This is the correct way, but I always forget the direction. When I rewrapped some bars yesterday, I just looked at another bike I had near it, and now both of them are backwards.

Here's the park page on handlebar wrapping:

https://www.parktool.com/blog/repair-...ation-drop-bar

Not always.

Another important lesson from the parktool photos - always remember to wear sergical gloves when wrapping your bars.

^ I do it opposite of that, wrapping under and out rather than under and in..oops I guess. Seems to work out fine though. I don't use anything but cloth tape, my new favorite is Newbaums. Nice thing about cloth tape (besides the minimal feel which I prefer over thick tape, which causes me hand fatigue) is that it isn't as picky about how you wrap it. Cork tends to be more finicky in my experience.

I usually wrap bars from the top down. I never have a problem with curling or coming loose. I prefer non-adhesive cork tape. The plugs hold the tape at the end. No electrical tape is needed and it looks really clean. I start at the front and go over.

As others have also said above, I wrap in different dirrections depending on the tape. In most cases I start at the ends and work toward the center so as to avoid curling on the bends. For Benotto tape and, I like to finish with heat and/or super glue for a clean look. For cork or modern tape such as Fizik microtape (my current favorite), I taper the end of the wrap so it has a clean edge at the center. For cloth tape, I go center to end (just like Eddy!) and replace if/when it starts to curl.

It is important to wrap in the clockwise/counterclockwise direction described in the Park Tools link. This is so when you are pulling back on the tops (such as when climbing), you twist the wrap tighter. If you wrap the wrong way, pulling on the tops will help to loosen the wrap.

I've wrapped all my bar tapes since the 80's going away from the brake lever down and up towards the stem.
Pressure from the hands in my case goes downwards and out when on the tops of the bar and then, when on the drops, there a tendency for pressure from the hands to push forward a bit from the ends of the bar, so for both top of the bar and drop positions, I do not have any tape edges that can curl up and start gaps. It works, as I never saw gaps on my bar tape ever again since I started this method of tape installation back in the early 80's.......

Chombi

i couldn't disagree more with the park instructions. i start from the end and wrap from inside out, so hand pressure is always applying tightening pressure. once you arrive at the lever, you wrap from outside, over the bar, then under and around the outside of the lever and back under, making the 'figure 8.' this puts you in position to continue on the top, wrapping from in to out toward the stem clamp.

i always apply two pieces of electical tape (one atop the other) to complete the wrap, but i cut the width of the black e-tape in half, 'cause a thin finish looks more elegant.