Though, MapBox is extremely expensive if you require SSL support (because your site is on SSL) and you are a startup. You can't even solve it yourself by performing the SSL termination and proxying the requests as that is prohibited in their T&Cs.
But at least they exist and offer a really beautiful map style based on the OSM data. Still US based though, but they also provide TileMill so you can host your own (though not using their very good Streets styling).
On the data side there's the recently launched http://opencagedata.com (disclosure, I'm the founder).
The point is with OSM there's more than one way to do it. You can dive in, get your hands dirty and do it all yourself, or work with a rapidly growing ecosystem of service providers who do the work for you at a cost. With private geodata / map providers, be they internet giants like Goog or national mapping agencies there is their way or ... their way.
Not to navigate by car, by bike, by foot. Not to show advertiser bubbles, or utilities.
Just a clear communication of "The point in question is in this neighbourhood, at that point.".
For me, that's the beauty in MapBox's Streets style... it does that one thing really well. Retaining enough countryside detail to make location recognition very good, and it works brilliantly in a city. Yet at the same time it's neutral enough to look great no matter how bad the design of the web-site it appears on.
I definitely prefer non-US, and non-giant mapping providers, but there's a lot to be said for cartographers who design maps to be useful generically for location recognition rather than anything else. I strongly feel that this is what Google Maps got so right, and is also why MapBox will do very well.
More than the tech, design matters.
We look at a map of our town or city, and the main roads in and out are the spines - everything is off one of them. If you turn those white, and remove the emphasis, the map becomes far less readable.
It's fairly easy (days work) to set up a Geoserver web map server to provide the data you need as a Web Map Service. You could use parent's data.
People should note the GetFeatureInfo interface that WMS provides for asking about the entities in a particular part of the map - click a house, yield the address and owner as XML (if you have that data).
Then you'd use openlayers to implement the web map on your site.
A 'roll your own' solution like this is only a good idea if you want to do something special, but an off the shelf solution constrains what you believe you can do. Imagine if every start-up was doing their site in wordpress.
I personally find that the users prefer the CloudMade API in terms of the quality of results that come back from geolocation searches.
The maps work fine, and the site could do with an update... but where CloudMade struggles is the design of the maps. At certain zoom levels (quite zoomed in) and within particularly dense areas (centre of Paris and London) they're just ugly. Which would be fine were it not for the fact that where there is high-density there is also a lot of users.
Both CloudMade and MapBox allow you to run custom styles... but unless you are a designer and/or cartographer who knows what you're doing, you're likely to make a hash of it.
Getting a good design for maps is very very hard, making something ugly is shockingly easy. Neither CloudMade or MapBox can prevent this, but at least MapBox's default is really quite beautiful.
Not really satisfying
Google Maps for mobile devices fundamentally fails because mobile data coverage is far from ubiquitous or reliable for something that important.
The only slight downside is there is a limit to how big a single downloaded map can be. So if you want to download all of Europe you have download it as a whole bunch of smaller maps and switch between them rather than a single big map, but realistically I've never run into problems with the size limitation
If you have the offline map, you can still do this even if you can't use the GPS navigation feature.
I can make coffee by pounding my own grinds and boiling water over a campfire. But if I wake up expecting to turn the coffee maker on and can't, it can throw off my day. Further Google Maps is a terrible, terrible way to handle navigate on a smartphone, especially in a dense urban area with layers of highways.