I doubt a definitive list exists.
But here is an algorithm to create your own list: What altitude-based things make climbing a peak require gear?
At what altitude do problems in step 1 start occurring?
What non-altitude-based problems might cause a climb to require gear?
What peaks nearest me are this height or less?
Here are my personal answers to those questions:
Snow and Oxygen are the altitude-based problems in mountaineering.
At 20,000 feet (6 km) or taller, most peaks are covered in ice all year round.
At 16,000 feet (4.9 km)
there is so little oxygen you need to take several days to acclimate.
Glaciers, steep trails, and scrambles so steep there are no trails
mean you have to break out crampons and/or rope.
These days I refuse to do anything that includes the word "Crevasse".
Look on Mountain Project .
Sure,
you can hike Kilimanjaro (~20k ft / 6 km) without any gear.
But it takes like a week to get acclimated to the lack of oxygen; how annoying!
So, in my opinion, pick peaks under 16,000 ft (4.9 km) and hike in the Summer.
If you live in the continental US, all peaks outside of Alaska are under 14,500 ft (4.4 km).
If you're in Western Europe
it's the same deal, there are no peaks over 4.9 km (16,000 ft).
So look on Mountain Project for all the mountains near you and see if they have permanent glacier-cover.
That will require crampons.
See if other hikers break out rope because the top is crazy steep with sharp drop-offs.
Nothing to it, just read descriptions of the hike before you head out.
People will say if they think gear was required.
outdoors.stackexchange.com/users/767/theJollySin
Referring to @theJollySin's answer: In Europe the mountains aren't that high
but you still have to go over glaciers on most routes to the high summits.
So you need to learn some basic safety/rope skills.
And you can find really tough routes on smaller mountains, so you just have to read tour descriptions and check the difficulty level.
You need to search for a F-rated tour without going over ice (risk of crevasses).
Some guide books also mark tours/routes which are solely going over rock, so this would be more the style of tour you have to search for.
This is hiking on high altitudes.
If you go really high (above 4000m or even 5000m), like being said, you need some time/experience to acclimate.
And I guess there aren't lots of summits on these high altitudes which are technically that easy.
Kilimanjaro is a good example of a big but technically easy tour.
Mount
Ararat might be interesting too, also in terms of history and culture.
outdoors.stackexchange.com/users/2653/Wills
There's a book published by Cicerone called 'Europe's High Points' which lists the highest peak in each country, and provides a pretty good description on how to climb them.
There are plenty of easier ones to go at, as well as some more technical peaks (e.g. Mont Blanc)
outdoors.stackexchange.com/users/152/Simon Hodgson
I haven't seen anything like the Scottish guide books we have for Munros - the tallest mountains in Scotland, but as Scottish mountains are relatively small compared to mountains in the Andes, Alps, Rockies, Snowy Mountains, Himalayas etc but still have a lot of dangerous climbs, I wouldn't want to guess at how few large mountains are scramble-able (if we exclude Kilimanjaro, for example)
outdoors.stackexchange.com/users/66/Rory Alsop
According to Wikipedia : Aconcagua is arguably the highest non-technical mountain in the world, since the northern route does not absolutely require ropes, axes, and pins.
Of course, non-technical means just that.
It is still difficult and dangerous, as mountains always are.
It's nearly 7 km (6,961 metre) above sea level.
It's an expedition that may take around three weeks not including acclimitisation time.
There will be very little oxygen, even if you acclimatise at 5,000 metre for weeks you'll still suffer from altitude sickness.
Cold weather exposure is common and kills people every year.
Don't underestimate the mountain just because you may not need ropes or axes.
If you consider weather and oxygen conditions on Aconcagua to be to harsh for your list, then there is no definitive list, for the impact of weather and oxygen is gradual.
What mountain does or doesn't need mountaineering experience is relative.
outdoors.stackexchange.com/users/566/gerrit
I was wondering if there is a list of the tallest mountains in the world where you can walk or scramble up to the summit? As opposed to using even basic rope skills?
Is there a definitive list of the tallest mountains in the world that require little or no mountaineering experience?
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outdoors.stackexchange.com/users/122/Aim Kai
A definitive list may not exist. However, a book published by Cicerone called 'Europe's High Points' which lists the highest peak in each country, and provides a pretty good description on how to climb them. You are unlikely to find a definitive list, but guide books can be helpful.
There is unlikely to be a definitive list. Guide books on peaks can be useful.