Depends on what photos you plan on taking/your style of photography. On all my recent holidays, while I very occasionally wanted something with more reach, I used something on the wider end about 70-80% of the time. When I went to New York, I took a 28mm and a 50mm lens (with a film camera mind), and when I went to China and Hong Kong, I took my E-P5 with 17mm and 25mm lenses (35mm and 50mm equivalents respectively). Personally I found them enough, but YMMV.
Also about depth of field, don't forget that Micro Four Thirds are considered smaller sensors. That alone means you have a deeper depth of field (i.e. it is harder to get shallow DoF). But if you have a fast wide angle lens (like the 12mm f/2 or 17mm f/1.8 which is borderline wide angle, but still on the wider end), even if you shoot wide open, if you're shooting a typical landscape shot (with everything all pretty in the far distance), just about everything is going to be in focus. It's hard to get shallow DoF with a wide angle lens. The only way you're going to get it is if you shoot a subject which is really close to you. Also having a fast wide angle lens means you can shoot at night wide open, which lets you keep the ISO down (thus better image quality).
I hope I'm not boring you (or anyone else) with all this.
Thanks!
Now I'm just struggling to decide whether I should get a 17mm or 25mm lens, I was sceptical of prime lenses at first but now with some researching I want one...