Helping people with computers... one answer at a time.
Legally downloading music files gets surprisingly complex. There are many sources, both legal and not, and they're difficult to distinguish.
This is a question that has been bugging me for a long time: do you know a decent site from where I can download legal MP3 files? I ask this for a relative, because I myself am old-fashioned: I either buy the CD or get the CD from a national library here in the Netherlands with 300,000 titles. I then rip the CD to Ogg Vorbis format and listen to it on my computer (Ubuntu Linux with Banshee music player) or on my BlackBerry (which, surprisingly, plays Ogg Vorbis). But this relative of mine asked me how he could download music to create and burn his own CDs. If someone wants to download music legally, I would suggest they look at iTunes, but with DRM and all that, I don't know if you can burn CDs from that.
My experience is that iTunes will let you burn some songs to CD, but not others. As I understand it, it's up to the music publisher of each song as to whether that's allowed. (And yes, it's frustrating when it's not.)
Unfortunately, I don't have a specific recommendation for you in the Netherlands. I'll touch on a few possibilities for getting music legally, but it's a surprisingly difficult question to answer in a useful way that makes it clear what is and is not legal.
I also want to address something in your question that has me a little concerned:
You might already be violating copyright law.
A great rule of thumb is that if you have to purchase it and you're purchasing it from a legitimate vendor, then it's almost certainly legal.
So vendors like iTunes and Amazon.com are great sources for legally available music. In fact, Amazon makes digital music available in MP3 format and because it doesn't require iTunes or any other application, it's my favorite source of music.
I honestly don't know whether Amazon sells to the Netherlands (amazon.nl redirects to amazon.co.uk, so I'm not sure of the relationship there). But I would look to major retailers and music stores for equivalents there.
A great rule of thumb is that if you can get it for free and it's from a popular musician on a major record label, then it's probably illegal and in violation of copyright.
Popular music available using bittorrent, for example, is almost certainly being downloaded illegally and we've even heard of record companies suing those who do so.
There are probably many download sites where you can download music as well, and the same rule of thumb probably applies.
Unfortunately, those are the only rules of thumb and can't be applied broadly. For example:
There are subscription sites where you pay to "join" to gain access to downloadable music. Some of these sites are not legitimate and you're left downloading illegally pirated music, even though you "paid".
There are subscription sites where you pay to gain access to downloadable music which are legitimate.
Some musicians make their music available for free by choice; either it's a limited-time incentive or an introduction. The best source for this is probably the musician's own site.
Some musicians make some of their music available for free. Again, the best source for this is likely the musician's own site.
The net result is that it's often very difficult to understand what is and what is not a legal source for music.
You indicated that you borrowed CDs from the library and ripped them to music files on your PC.
If you then kept those files when you returned the CD, that is very likely a violation of copyright law.
The CD available at a library is meant to be borrowed and returned. When you return it, you don't have it any more. What you've done is you've made a copy of the CD which you then kept.
Unless the artist has explicitly allowed it (which is unlikely in most cases), that's almost the very definition of a copyright violation.
It's possible (and this gets into picky details) that the mere act of ripping the CD might be illegal, but I suspect ripping, listening to, and then deleting the files when you return the CD to the library would at least meet the intent, if not the letter, of copyright law.
I stick to a known retail vendor, Amazon.com in my case, from which I can purchase my music and then check out individual artist sites for things that the retailer either doesn't carry or that the artists might offer. That keeps me safe and legal.
Unfortunately, I don't have a specific retail vendor to point you to in The Netherlands, perhaps readers there will chime in with legal suggestions.