What is this weed? It is what I mostly encountered when cleaning a bed of flowers after the winter here in Central Europe. The weed has blue flowers (approx. 0.5 cm in diameter) and grows mainly horizontally and close to the ground. It is also simple to tear out, a bit like chickweed in this way.
That's a type of Veronica, I'd estimate Veronica chamaedrys based on flower colour and amount & shape of foliage.
It's considered a weed by many gardeners, but as I personally like the flowers, I tend to disagree (or agree to disagree...).
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2Clarification: it's not considered a weed in my entire garden, but in nevertheless try to keep it out of certain beds :) – Drux Apr 23 '15 at 15:09