Mark and DCTLib already posted a link to official EU guidance on this (+1 to them) but it might be useful to clarify how these rules are intended to work.
Firstly, there is a fundamental difference between goods that have never been imported in the EU and things you take with you out of the EU and want to bring back in but that were originally bought in the EU. You might have to pay taxes and duties on the former but the latter do not need to be taxed again. In theory, customs officers can however ask you to produce some evidence that you did in fact buy them in the EU. Many countries also have a temporary export procedure to facilitate such reimports (especially for expensive equipment like computers, professional cameras, etc.)
So if you travel with a smartphone, a tablet and a laptop, they are probably worth more than the duty-free allowance but that's not really relevant (that's not the purpose of this allowance). You are allowed to reimport these items because duties and taxes (especially VAT in this case) have already been paid (the only potential issue is proving it).
Secondly, you do have the right to import some things as gifts or for your personal use. That's where the allowance comes in: As detailed in the EU page mentioned earlier, the total value of all the goods sourced abroad must be under EUR 430 (that's the price before taxes so one iPad is most likely OK but two tablets probably not). Both conditions must be satisfied: The value must be under the threshold and the importation must have no “commercial character”. There is no allowance for goods you intend to resell and no provisions to import expensive things tax-free and without paperwork only because it's for your personal use.
The allowance is designed to give you a bit of leeway for small gifts and to avoid ridiculously unenforceable rules that would theoretically require you to declare anything you bought abroad even if it's only a toothbrush. But it's not designed to allow frequent travellers to circumvent VAT and import duties for all their large purchases. All expensive goods (electronics, watches, luxury clothes, etc.) manufactured elsewhere and used within the EU are supposed to have been declared at some point, either by a professional importer (if you buy them inside the EU) or by yourself (if you shop abroad).
Thirdly, there is some gap between what's allowed and what you can do in practice. I have crossed the EU external border countless times with an expensive company-issued laptop, occasionally with boxed electronics goods or with wine and alcohol (within the allowance) and I have rarely been searched or asked anything. While I always scrupulously follow the rules, I could certainly have taken a brand new laptop or something else over the limit and gotten away with it and you will find many people who did just that.
EU borders are more open in this respect than many other borders I know (including US borders). There should be at least a passport check (except in the case of Switzerland) but it's not uncommon to enter without being questioned at all by customs. Enforcement is based on punctual searches, deterrence and tips by informants, not on checking everything that goes in. That's also why customs officers mostly do not bother with things like a single laptop or tablet without packaging.
Because of that you might actually get away with buying expensive goods in the US and bringing them back to the EU. But that does not change the rules. I even have a relative who got into trouble once for carrying six baby napkins with their labels (they were obviously well within the allowance value-wise but the customs officer ruled that nobody would need six of them so it was an illegal import - seriously). YMMV.