I'm really into hiking during the last few years. Now I want to climb the highest mountain in Europe that is accessible by a hiker without any alpine tour experience. That means I have no problem walking a whole day or climbing over 2000-3000 meters in one day, but I'm not used to glaciers, or any equipment that includes ropes or climbing irons.
So I assume that in Africa, my goal would be Kilimanjaro, but what mountain and starting village should I travel to if I want to stay in Europe?
Assuming you're also exluding mountains only accessible by via ferrata, the highest one I've heard of is Mont Taou Blanc (3438 m) in Italy near the border to France.
Here's a video of the ascent. The most difficult/dangerous part can be seen at 1:40 - and you can see that it's a very popular tour.
I did some research and it seems that Inneres and Üsseres Barrhorn in Switzerland are the highest mountains in Europe that can be reached by hikers. This is also mentioned on the English Wikipedia page. The German Wikipedia page has more information about that. On hikr.org, a very popular hiking platform in Switzerland, it is also mentioned that the Barrhorn is the highest moutain which you can reach by walking. Unfortunately the information is only available in German.
In Europe you have several options, often encompassed by the Alps.
While you can use a tour, often the tour suggestions are merely good idea for you to use. But they do at least let you know if it's able to be hiked without any climbing gear.
You can hike in the Italian Dolomites, the Carpathian Mountains, Bulgaria, Transylvania, the Fjords of Norway and more. Some descriptions of these hikes are on Mountain Hiking Holidays.
More on getting to the Tatra mountains in Poland and Slovakia.
Here are the 5 best day hikes in the Swiss Alps.
EDIT:
And if you just want a single mountain, consider the top 10 tallest mountains in Europe.
The German site linked to in Roflcoptr's answer mentions an even higher mountain in France, the Aiguille de la Grande Sassière (3751 m) and claims this is definitely the highest "hiking mountain" in Western Europe, but cautions that the ascent includes some "light climbing" passages, and depending on the weather the final ascent might be ice-covered.
I did something similar last year. From Zermatt a hiker can easily reach the Oberere Rothorn and the Mettelhorn, both 3,400+. The Mettelhorn is probably my best hike ever. 1800 metres ascent, a harmless glacier crossing (had no axe or crampons), and a wonderful view!
My personal record is the Stockhorn from Gornergrat, at 3,532 on the newest map, but I thought it was 3,525 when I did it. The route is annoying in places but it's quite doable, and puts you surrounded by glaciers on three sides.
I have my eye on the Barrhorn for next season.
Sweden's highest mountain Kebnekaise is accessible by foot though it is not that high (only some 2106 metres). My co-blogger Hardy did it and wrote about it.
If you want to climb the highest mountain in the UK, that would be Ben Nevis with ~1344m. There is a city nearby called Fort William and the surrounding area is stunning! Especially going from Fort Williams to the west coast by train is a great ride and there are many lochs and hills to explore.
Alternatively in the Isle of Skye in northern Scotland there lies a mountain range called the Cuillins, it is said that the hardest hikes in the UK go over the Black Cuillins, hard due to the strange shape of the mountains. The landscape on the island is amazing as well. Very thick and old tolkien-esk forests in the south and the rocky Cuillins in the north.
Not quite extreme alpine climbing, but if you want to avoid the people and enjoy a beautiful landscape than this might be the thing for you.
I have one that only requires hiking boots during the entire climbing season and slightly beats the Barrhorn: Monte Vioz in Italy, on the border of the Lombardy and Trento regions, at 3645 meters.
The standard route, SAT number 105, is from the village of Pejo on the Trento side, and is a simple mountain hike. There are a couple of places with fixed ropes but even they are not needed. It is certainly a lot of altitude gain, over 2000m, and if you're not used to >3000 meter altitudes, it might make you feel dizzy, but as long as that is something you can deal with you should be good. There might be a small amount of snow at the summit in early summer, but nowhere near enough to require crampons. Note that the approach from any other direction is more challenging and involves glaciers.
There is also an alternative route, 105A, which joins the main route at around 2900 meters. This is connected to a cable car going up to nearly 3000 meters as well as to Rifugio Doss dei Cembri at around 2300 meters, from where there is a wide network of easy footpaths and gravel roads. This route is actually slightly trickier, with lots of loose rocks. Also nothing you need equipment for, but I saw lots of families with small children trying to walk through it (presumably since the altitude difference is much smaller if you take the cable car), and that seems somewhat inadvisable to me. I don't know if this alternative route used to be simpler, as there have been rockslides here.
Depending on what you consider the boundary of Europe, Mount Elbrus can be considered the highest point in Europe. At 5642 m, it's considerably taller than Mont Blanc (4810 m). The standard route is pretty nontechnical, and requires only an ice ax and crampons.
