i've actually only travelled in Holland, but i think it should be simlilar in Sweeden too. and hopefully you'll get some native responses too...

but renting a bike should be super-simple in the Netherlands and there are rental shops in almost every train station. and it is pretty cost-effective as they rent lots of bikes so the price is decent.

but, one thing to remember is that the common bicycle in Holland is a big heavy city bike that most cycling enthusiasts would consider archaic. my girlfriend and i rented a tandem and it weighed something like 50lbs with no suspension or anything. we rode what i consider a modest distance (like 30-40 miles) one day and i was dead-tired even though it was flat... either my girlfriend was really lazy or the bike made a huge difference, or both! on the good side, most bikes come with fenders, racks and lights, often a bell.

if you are used to riding a fast quality road bike or lightweight suspension mountain bike then it may be much more difficult to find - i was surprised that about 90% of the bikes in Holland looked like they were about 50 years old -- then i saw trhat the new ones in the shop were still sold looking like that - heavy.