Munich to Rome by train (avoiding tunnels)

Inspired by @gerrit's answer, this one has one tunnel that is 5865 m long (and can be avoided with a 30 minute bus ride), but otherwise all other tunnels are much shorter.

• Roma-Firenze-Bologna-Milano: you will probably have to take regional trains, as the high-speed line has many tunnels: Roma-Firenze has 5 tunnels over 3 km (longest 10.5 km), Firenze-Bologna has 7 tunnels over 3 km (longest 18.7 km). Bologna-Milano seems to be relatively devoid of long tunnels. I won't go into details here as there are probably many different options depending on how much sightseeing you would like to make.

• Milano-Lecco: via Carnate: 2 tunnels (2228 and 2242 m), or via Molteno: no tunnels apparently.

• Lecco-Tirano: 6 tunnels, but the longest is 1395 m.

Note that you can ride from Milano to Tirano directly, but that will take the line via Carnate with its two 2.2 km tunnels.

• Tirano-St Moritz (Bernina Railway): 11 tunnels, but the longest one is 689 m. UNESCO World Heritage site.

• St Moritz-Thusis-Chur (Albula Railway): over 40 tunnels, but only one is significant, the Albula Tunnel which is 5865 m long. The second longest is only 698 m, and many are just a few couple dozen meters long. UNESCO World Heritage site as well.

The whole Tirano-Chur stretch can be done with a single train, the Bernina Express.

If you want to avoid that single tunnel, you can use a bus from La Punt-Chamues-ch Railway Station to Preda Railway Station, it goes over the Albula Pass, takes less than half an hour, but only runs from end of June to end of October.

• From Chur, there are several options, the simplest one involving just one change at St. Margrethen. There do not seem to be any tunnels around, but I haven't checked extensively.

Note that if you check itineraries on the CFF/SBB website (the Swiss Federal Railways), you can view the full route on a map, and once you zoom in enough the (OpenStreetMap-powered) map will show you tunnels.

Final note: whether you take the train all the way or use the bus to avoid the Albula tunnel, it will take you quite a while to do the whole trip. But you will have some incredible scenery on the way!

Since the highly upvoted and currently accepted answer involves buses, a slight change in transportation mode seems to be acceptable. Therefore I suggest flying.

Looking several weeks out, Lufthansa has several offers for under 90 EUR round trip with nonstop flights of about 90 minutes each. Even with getting to and from airports and passing security, that trip is well under a day.

The first one I checked is scheduled to use an Airbus A319 and Airbus A321-100/200 for the routes to and from respectively. The inside of the plane cabin might be bigger than the inside of a train or bus, and the specific seat area might be comparable to a bus (maybe more area if you pay more).

Actual costs will depend on when you want to go, when you're booking, and a surprisingly large variety of other factors.

Planes do even worse than you in long tunnels, so you're not likely to have any of those on the flight. The reduced remaining challenge is getting between the airports and your origin/destination without long tunnels, which seems likely easier, though the question doesn't have enough information for us to address that.

Challenge accepted. Since you posted the question of how to get to Budapest from Munich a while ago (How to avoid the huge tunnel at Vienna when travelling from Munich to Budapest by train?), I will take it from there.

You can take the train as described until Vienna. I suggest doing this on day 1, so that you can spend the night in Vienna. This is because I will now take you through Slovenia into Italy. There is only one viable train going to Trieste from Vienna which leaves Vienna at 7:58 in the morning and gets you to Trieste with a change in Ljubljana (takes 10:55 hours). Then you can take trains as described in other answers to Rome. I doubt you will make it on that day, though. Make sure to go via Graz and not via Villach since this will mean a lot more tunnels.

The line from Vienna to Trieste only sees one bigger tunner, the Semmering tunnel which is 1500m long. Otherwise there are only few short tunnels. So the route is (Munich - Wienerwald tunnel bypass -) Vienna - Graz - Ljubljana - Trieste (- Bologna - Rome).

If you want to take this further, you can even go to Budapest and take the daily train to Ljubljana from here. This avoids any tunnel on the route (Budapest-Trieste is 14:33 hours). This would be the shortest way around the Alps avoiding long tunnels.

None of the options will allow you to make it in one day, though.

In case the comments to the question disappear if the OP is happy to pass through tunnels while asleep the NightJet from Roma Termini leaves at 1858 which for most of the winter is dark and arrived at München Hbf at 0819 the next day. It would be best to book a single sleeping compartment so you can be sure you can pull the blind down to avoid seeing anything while passing.

Of course this will not work if it is the knowledge that one might be in a tunnel which is the trigger rather than knowing one actually is.

You could avoid the Alps and their consequent long tunnels by going Milan-Nice-Lyon-Strasbourg-Munich. I haven't researched the details of the tunnelling on this route, but there aren't any large mountains to tunnel under. (Lots of short ones though).