My kids enjoy playing "The Alphabet Game", "I'm Going on a Trip", and "20 questions".
The Alphabet Game This is a version of I Spy. Each person has to spot something that starts with each letter of the alphabet, starting with the letter A and going in order. Those with the sharpest eyes tend to reach Z the quickest, but only if they are paying attention. (Example: A - Ants, B - Bird, C - Pine Cone, etc. ) Kids, and older people, with smaller vocabularies and knowledge learn quickly from the game and soon compete well against Alphabet Game Veterans. For example, when someone spots a porcupine quill for the letter Q, younger kids will remember what to look for in the future for that letter. Each player goes through the alphabet on their own and is not allowed to leapfrog off what another spots - and whoever spots it, claims it. So, if everyone is on C and a single Clark's Nutcracker flies by, whoever spots it first, and names it, gets to move on to D. A sharp-eyed and knowledgable player can reach Z while another is still back near the beginning at, say, the letter F. They also have to spot the object/animal when they need the letter, otherwise it doesn't count. Adults have no advantage in this game over an attentive youngster. Also, the rules can be adjusted for hard letters. For example, if they are allowed to spot items carried by the group, then Z is really easy: just spot a zipper on someone's pack.
There's only one winner per game, but the game cannot start again until everyone has either finished or quit (usually a player wants to quit only when they are really tired). Those who have finished will usually start pointing things out, but not saying anything, to help those that are lagging - all so they can hurry and start the game again.
Caution: This can create diversions on your hike. For example, if everyone is on the letter F right as the trail nears a creek or marshy area, the players will probably scatter out looking for Fish or Frogs. But that usually just adds to the fun, doesn't it :)
We also do a version of this game when driving, trying to find the alphabet letters on road signs, license plates, business signs, even mountains (towns around here like to put giant white letters on mountains, just the first letter of their town). We've tried to come up with other versions, too, like picking a book that we've all read and taking turns naming a character whose name starts with the letter our turn falls on. But the only book that has worked out with has been the Harry Potter series (it was lots of fun the one time we played it, but it was just dull the next time we tried).
I'm Going on a Trip This is a memory game. The first person says "I'm going on a trip and I'm taking a ________. They name something. The next person repeats the statement and adds one more item. The game continues, each person adding a new item at their turn, until one player forgets something on the list. Everyone pays attention and tries hard to remember because they want to catch another player saying something in the wrong order or skipping an item. When you get it wrong on your turn, you're out. Last person still in wins.
20 Questions I think most people know this game, but here's my version for whoever doesn't know: Someone imagines something (usually something they just spotted). The game starts when they've got the image in their head. Then anyone can ask questions - only yes/no questions. The person being asked the questions must always answer honestly (or no one will ever want to play with them again) and cannot give any help or hints (we break this rule if younger kids are playing). The game ends when someone correctly guesses the item. The winner then gets to choose the next object and the game starts over.
Singing This was mentioned above, but I'm repeating it here only because it's really not very popular very often. I think it takes a lot of energy (and oxygen). Plus, it sometimes just sounds like a bunch of noise - especially to other folks out there in the woods. About the only time we sing is if we're really in the mood (lots of energy) or somebody's scared of something (like it's getting dark and we're still hiking).