Except for one, which I'll get to in a bit, all the commands I use for my Hysson (in my avatar) are the same used in the obedience classes we took when he was younger and still use around home.

"Come." Or the equivalent. Actually, so many of us use the word "come" for encouragement (such as "come on, let's go for a walk") so much that we really should use another word to call the dog. I know that's why my Hysson considers it an optional command! (Using "OK" to release the dog from a stay has the same issues.) Fortunately, "heel" works (so far) 100% of the time. IMHO, if the dog doesn't come (or heel) every time you use the command, regardless of distractions, he should be on leash!

"Heel," "Sit," "Down," "Stay" are of course highly important. "Wait" if you want him to halt momentarily (such as waiting for you to exit the tent first). "Walk" (as opposed to "Heel") means that Hysson can walk as he wishes anywhere within the length of his leash, but without pulling. Off-leash, the command means he has to remain within 6 feet of me. Sort of a "remain close" idea.

One very useful command on the trail, particularly where leashes are required or (because of frequent traffic) a good idea, is the "Finish" command. It's used to get the dog from in front of you (in obedience, from sitting facing you after the recall routine) to sitting at your left side ready to "Heel." There are two types of "Finish"--different people use different commands for each. One of them (my classes used "Around") means the dog walks around behind you, starting on your right, and ends up sitting at your left. If he's on leash on the trail, the leash will be wound around your legs and your trekking poles. (If he's off leash, he may go quite far away when behind you!) The "Finish" routine to use on trail is where the dog walks to your left, turns his hind quarters around with his head next to you, and ends up sitting at your left side. (It's easy to teach with a treat in hand.) That gets the dog from in front of you to your left side without any entanglements!

Another useful command is "Leave it," when the dog is involved with distractions such as food or carrion. It can be lifesaving in some circumstances (such as dead fish at the edge of a stream, which at least here in the NW carry bacteria that can cause fatal illness in dogs).

The one command I "invented" for Hysson for hiking/backpacking use is "Behind." That means he is to walk directly behind me on the trail. I taught it to him for two reasons. First, I don't want him to run ahead of me, especially where there's a good chance of meeting oncoming hikers or horses or maybe wildlife around a blind corner. The main reason, though, is when he walks in front he likes to be a few inches in front of me and then stop dead if he encounters a fascinating smell. I haven't yet fallen over him, but some day it's bound to happen! It's also very annoying when I'm trying to keep a steady pace. At home we practice this command on our daily exercise walks. Then there was the time that Hysson went ahead of me on a log across a torrential glacial stream, and then came back out to me in midstream, no doubt wondering why I was so slow. The log was narrow enough that I had to back up to the bank I'd left so I could get Hysson turned around. Since then, it's been "Behind" for every log crossing!

In the cases you describe, I just tell Hysson to "heel" and either grab his traffic lead (18-inch lead used for agility training, in Hysson's case the nose band part of his Gentle Leader head collar) or put on his leash. I of course give him good scratches and praise while doing that so he doesn't regard being leashed as a punishment! The reasons for leashing him for these occasions are to overcome distractions (considerable if the oncoming folks also have a dog) and mainly to reassure oncoming hikers who are nervous about dogs (these include a majority of children and more than a few adults who have been bitten in the past). I know that horsemen also feel much more comfortable if the dog they meet is on leash. Hysson is quite calm around horses, but of course the horsemen we meet don't know that!

Speaking of agility training, I thoroughly recommend a beginning agility class for hiking dogs. Once your dog has become confident running through tunnels, going over jumps, jumping on and off a table and, above all, walking across a teeter-totter, he won't be at all nervous about going over/under deadfall or walking logs across streams (I know otherwise enthusiastic hiking dogs who refuse to do the latter). Your dog should have mature joints (or jump heights should be severely limited) and not too old (the activities could exacerbate arthritis). Hysson was a little over a year old when he took the class (the jumps were set really low). It was recommended as a transition to the third level--all off-leash--obedience class. It worked fine for that purpose, but I didn't realize until we got out hiking the next summer how much the agility class helped him be confident in rough terrain!