Well, not actually climbing, rather taking the cog railway two-thirds up the mountain and walking about half an hour up to the peak. It's a great trip though. I rode the railway from Zug along the lake to Arth-Goldau, and changed into the cog railway. Very beautiful, and if you ride all the way up, it's a mere 170m from the station to the peak. Even computer nerds like me with no physical fitness to speak of can manage those.
From the peak it's a great view over the Lake Lucerne, the Lake Zug and the Alps. The weather was fantastic, and not surprisingly there were some people up there, but it was far from crowded. There also seemed to be a quite nice updraught -- I've seen several paragliders and one hang glider frolicking around...
After having arrived at the peak I snapped some photos, read a little, chatted a bit on skype (decent GSM coverage up there!) and then decided it was time to go before I got seriously sunburnt.
All in all, a very pleasant trip. Next time I'll go down the other side to Lake Lucerne and go back via ferry. And maybe bring some sunblocker and better shoes (may boots are still in Graz and so I stumbled around in sneakers, the prototypical tourist).