My answer is "don't ask".
It's not so much that it's "impolite", but it's an imposition to them and potentially dangerous for you:
Belaying can take quite some time, so you're asking the person to give up a chunk of their recreation time to a total stranger.
It's not like you're asking someone to help for 30 seconds
You're putting your life in their hands, literally.
That's a big decision.
What if they're also a complete novice but feel embarrassed to admit it.
I wouldn't let anyone belay me unless I was confident they knew what they were doing and trusted them to do
it Don't go to a two-person sport venue by yourself.
What if you get to the cliff and no one else is there?
Find a climbing partner(s).
Learn together.
It can be rewarding and build a great relationship as you both improve.
You'll have someone to share your climbing highs and lows with.
outdoors.stackexchange.com/users/9209/Bohemian
From my experience, the simple act of asking won't be perceived as impolite.
There is a good chance that people will let you join them, but be prepared to accept "no" as an answer just in case.
It would be impolite to press on and try to get them to change their minds, but if you politely accept the "no", you should be fine.
(I assume that you actually want to join the group and belay them, too.
If you just ask for a belay and don't offer anything in return, that might probably be seen as rude.)
But this highly depends on the people and on the circumstances; for example, on routes that are well equipped with bolts, I would be more willing to accept new partners than on challenging multi-pitch trad climbs.
The same goes for the perceived experience of the potential partner: People that seen experienced and want to try a hard route that I'm also interested in will more likely get a positive response than obviously inexperienced people that beg me to put up a top rope on a UIAA 5 for them.
Of course, this also applies the other way: Make sure that you are comfortable with the people in the group belaying you.
See Vetting belayers at the gym? ; most things also apply outdoors.
In short: Asking won't hurt, and trying to make sure that you would fit into the group will maximize your chances of joining them.
outdoors.stackexchange.com/users/5657/anderas
Where I climb (New Mexico, USA), I think it would be impolite to walk up to a stranger outside and ask them out of the blue to belay you.
I have been awkward position of being asked to belay someone I don't know / don't want to, and it is certainly uncomfortable.
However, it's certainly not impolite to go to a cliff looking to find new climbing partners or join a group of climbers.
Approach them, start a friendly conversation, and explain that you're looking for climbing partners but having trouble finding them, or whatever the case is.
You might say you enjoy the area and like to come out even when you don't have someone to go with.
This gives them the opportunity to offer to belay you without putting them in the awkward position of having to refuse.
Also, you might offer to belay before requesting a belay.
Find an odd-numbered group that seems to be about at your skill level and offer to belay whoever is waiting around.
They may be very happy for that
and then they'll belay you after that, and you may have made a new friend.
outdoors.stackexchange.com/users/9213/foobarbecue
I think even asking sometimes can be impolite.
Some people just have a hard time saying 'no', even if they don't want you there.
If there's a good chance they wouldn't want you in the group, don't put them in a difficult situation.
Probably Don't Ask: A group of 2 climbers obviously on a climbing date
An even-number group of climbers who look experienced and setup quickly.
They don't need a third/odd person to slow them down
Any group of climbers that are having a great time catching up, haven't seen each other in awhile, or sharing inside jokes.
You'd be disrupting the social experience for them as they try to accommodate you.
If you are inexperienced enough, such that you would need them to coach you through different tasks.
If you are missing equipment that you would need to borrow from them.
If you sense a great skill imbalance (you are much less experienced than they are), you probably aren't welcome.
If you are much more experienced, you might be welcome if they need a lot of help.
But you could also be unwelcome if your presence makes them feel intimidated or feel rushed.
If you wouldn't feel safe on their anchors or being belayed by them.
Okay
To Ask (assuming situation doesn't fall into previous list): An odd-number group of climbers that seem impatient about waiting around.
They would probably benefit from your belaying presence.
A group of climbers that are around your same skill level (so you guys can climb the same routes)
You have a necessary piece of equipment that they are missing, so no one can climb unless you all do it together.
outdoors.stackexchange.com/users/3345/shimizu
For all the reasons in the other answers, one probably should not ask to be belayed by another group of climbers.
There's just a lot of awkwardness involved, and a lot of strange risk in trusting someone with your life.
However, if you do want to try to get belayed by others, don't be afraid to use a social approach.
Go up to groups and chat with them a bit, show your interest both in the climb and in them.
There's a reasonable chance they will offer to let you join, if you play it right.
And if they don't, you still spent your time networking with the climbing community.
Who knows what you might learn!
outdoors.stackexchange.com/users/8208/Cort Ammon
I'm a beginner climber.  There are many climbers all over my area (doing cliffs).  Would it be polite, impolite, or neutral, to approach groups and ask them if I could join them?  Maybe this is 'obviously' impolite, but I've had a group offer before, so I wonder if this is just part of climbing etiquette.  FYI - the climbers are from all different countries (lots of Germans, Australians, and others.)
Is it polite to ask other climbers to belay for you?
outdoors.stackexchange.com
<climbing><belaying><etiquette>
outdoors.stackexchange.com/questions/11405
outdoors.stackexchange.com/users/9206/HH- Apologize to Carole Baskin
It might be awkward and a strange risk to trusting someone with your life. In some areas, it may be considered impolite to walk up to a stranger outside and ask them out of the blue to belay you.  It's an imposition to them and potentially dangerous for you. Belaying can take quite some time, so you're asking the person to give up a chunk of their recreation time to a total stranger. There is a  chance that people will let you join them, but be prepared to accept "no" as an answer. However, it's certainly not impolite to go to a cliff looking to find new climbing partners or join a group of climbers. It is acceptable to look for new climbing partners, though it is best not to ask people to belay you for safety reasons.
Whether or not it is impolite, it is best not to ask because of safety reasons. It is acceptable to look for new climbing partners.