All you may need is a pair of comfortable walking shoes and maybe sandals if they’re your thing.
 
I spent 6 days in Amsterdam walking around in a pair of worn New Balance shoes.  I was on my feet and walking virtually the entire time.  Public transport was availiable but walking gave me more opportunity to explore.  Big mistake on my part.  Not even 3 days in I began to get severe pains in my foot.  I got a huge blister (that eventually tore open) on one of my feet.  Each night, upon my return to the hostel, I was literally limping from the pain.  Make sure you have comortable walking shoes in good condition. 

I need two pairs of shoes (maybe one pair of shoes and one good pair of sandals). If I don’t do some switching, my feet will complain. Younger people might find it different.
 
I totally sympathize with yojimbo, having done similar things myself. If you find yourself getting blisters, start taking care of them immediately with moleskin and band-aids. You can take some supplies with you, but if you don’t, be sure to spend the money necessary right away. And make sure your shoes are broken in, but not too old.
 
Keep in mind Rome in summer will be really hot and humid, and plan accordingly.
 
My favorite walking shoes are Merrell Jungle Mocs. My favorite walking sandals are Rieke, I think. And – I hate to admit it – but now and then I wear socks with sandals. And – lots of Europeans do this too.

Definitely depends on what you’re looking to do.  If you’ll be city-exploring, about the toughest hike you’ll make is the Spanish Steps, and as yojimbo and traveler said, you’ll probably only need a good (new, but broken-in) pair of running/cross-training/walking shoes.  I have Asics Gel Kayano 13’s.  Great shoe, very durable and light, good arch support. 
 
If you’re looking to do some serious hiking (as I am this summer), I’m assuming you’ll need something sturdier.  Now since I’ve never been backpacking across Europe,I can’t say just how bulky or inconvenient it might be to lug around hiking boots, but I backpack on the AT pretty often, and it’s essential to have hiking boots.  The soles of running shoes just aren’t thick enough to cushion against rocks without destroying your feet; not in the long run at least.
 
So it depends what kind of wear and tear you’ll be putting your feet through.  I’m torn because I run almost every day and my feet are calloused like a lion’s paw, so I think I could get by with my Asics…but I don’t want to press my luck.  I think Traveler had another good point, you can fix a lot of foot pain by rotating shoes when you can.
 
I’d recommend:
 
1 pair of either athletic shoes or boots.  One’s lighter and more packable, the other is durable and foot-friendly for the hiker.  Take your pick.
 
1 pair of sandals.  Those rubber/foam/whatever-they-are ones could also double as hostel shower-wear haha.
 
1 pair of something else.  Sperrys sound like a really good idea actually.  Comfortable, fairly light, and you could wear them out at night.
 
Regan

Sperry’s are probably fine if they offer enough support.
I wouldn’t take any shoe that I have not already worn for a full day and seen how my feet did.

I always just take two pairs of shoes, and alternate them.
What kind of footwear depends on what time of year.
The last big trip I took, it was mid-summer. I had a pair of Tevas, and a nicer strappy sandal-shoe (which was more rugged than it probably sounds).

Guess, it’s finally my time to jump on yet another “what type of shoes” discussion. So my two cents:

1. The shoes you bring should be suitable for the climate of the places you go to and for the type and the amount of walking you’ll do which are probably quite different from where you live.

2. The shoes you take on a trip should be well broken in, but not worn out. If you have a favorite pair of shoes you love to death, but it’s almost dead, get another pair of the same, or a similar model (style, construction, sole type) of the same brand. If you want to try something new, make sure you wear your shoes a lot before you pack them up, and they still feel comfortable.

As far as specific styles/brands/etc goes, to each their own.

There are a few brands (like Merrel, Solomon) that make hiking shoes that are light, comfortable, look reasonably stylish, have decent ventilation, but still protect you when it gets cold.

Personally I’m against sneakers. (It’s not because sneakers wearers are singled out as blue jean shorts/white t-shirt/baseball cap wearing Americans. If that’s who you are, you should have no trouble being identified as such.) Athletic shoes nowadays are very specialized (I love to run in my Nimbuses, but virtually can’t walk in them.) Ones that are not specialized, or marked as “walking shoes,” are usually nowhere close, in terms of comfort and durability, to hiking shoes in the same price range.

Sperry’s… On my last summer trip I only had room for one pair of shoes not counting shower flip-flops. I took my chances, figuring that if I go with Sperry’s I’d save space taking no socks either. They (or rather my feet) did fine for two weeks, in part because I did not have to walk for more then 5 hours in a single day. However on the last day before my flight back (to Canada), I’ve spent half a day criss-crossing Venice under the perpetual rain. By the time I had to catch a bus to Treviso, I’ve got sores on both feet. I guess next time I’ve got to be more careful.
 
I’ve never owned Keens, but next time I need hiking/walking sandals, I’ll probably take a good look at them. One time I’ve ended up wearing Birks for the most of my trip (back then everybody wore Birks) and they felt all right, but their soles wore out pretty fast. If you plan on wearing them every day for a month there will be no need to carry them back home. Finally I can’t understand those people (mostly girls) who insist that old-navy style flip-flops are the best shoes to wear and use them for everything, from hiking to clubbing. But again to each their own.

I like to bring a pair of sneakers and a pair of comfortable sandles with lots of straps. I always used to be against more than one pair of shoes (too much bulk), but, in reality, wearing the same pair of shoes everyday will start hurting your feet if you do a lot of walking. If you bring two pairs, at least you can switch it up a little bit to avoid blisters

I’d just throw out a recommendation against Chacos.  I love mine, but they’re heavy as bricks.  Took them on a hiking trip and I ended up regretting it.  Unless you’re one of those rain-or-shine Chaco wearers who simply can’t not wear them, there’s probably a better choice (Keens or Salomon boots or something else mentioned above). 
 
Really all you have to do is figure out what you’ll be doing day-to-day.  If it’s hotel-hopping via plane/train and checking out some local sights, you can probably bring whatever the heck you want, granted they’re decently durable.  If it’s up the Jungfrau for you, invest in something better.  Any outfitter store oughta be able to help you out there.  Just don’t let them sell you on the most expensive shoe—it’s probably overkill even for the Swiss Alps. 

For walking around towns for the most part if they are clean, Birkenstocks are ALWAYS such a help or just some comfortable walking shoes never did me wrong walking through the middle east.

I actually did Europe on tan Old Navy Flip Flops 2 years ago, a lot of hiking, and a lot of walking and still to this day I have no idea how i came back to the US with no blisters on my feet. However they broke on the plane ride home…

I’m trying my Keens out in Europe this summer, i took them with me hiking in the Idaho Panhandle in September and they worked amazingly well for being on my feet constantly. I recommend them on comfort and wearablilty when walking a lot and hiking!

I’m picking out some shoes and am looking at either Keens or merrells although Salomons look like nice kicks as well. I’m a die hard New Balance boy here in the states but I don’t know how they’ll treat me day in and day out for six weeks in Europe. I’m definitely brining some Old Navy Flips for shower shoes. Would it be overkill to have some Keen flips and hiking shoes as well? Probably I imagine but just wanting peoples thoughts.

I don’t take hikers. Most tourists never get off city streets and even though I usually end up with a serious hike or two, I’ve never been on a European hiking trail that wasn’t easy to handle in sneakers or sturdy sandals. I’m with Lpeabbles — sneakers alternated with sandals sturdy enough that you can spend all day on your feet with at least the extra weight of your day pack.

To me, the issue is the extra weight. I could probably handle all day on my bare feet, but add the weight of a even a day pack with guidebook, camera and misc. and I need sturdier shoes.

I like New Balance shoes at home because they’re just about the only brand that makes really narrow sizes in casual shoes. I don’t take my New Balance shoes to Europe because they’re too sturdy/high cut, too heavy and get too hot. I prefer toting as little as possible, so I take low-cut Skeetchers (or similar low cut but sturdy) and Clark’s sandals.

Depends on the season you are traveling actually,but since there is a lot of snow in the cool seasons..it is recommended that you have well covered sneakers so that the foot is comfortable and warm and does not catch a snow bite.

Certainly depends on the Latitude and the altitude. Most of Europe as very little snow — but it is cool, damp and rainy.

I’ve taken some very comfortable New Balance shoes on trips, alternating with sandals (something with a bit of cushion). I will probably do the same on my next trip. The NB I’ve had have lots of support, and I’ve always had back luck with Sketchers.