I worked in H&M for years during my student days. I loved when there was a new delivery of make up! (I just had to make new testers for the *cough* customers... not for me to play with oh no) Some of the cosmetics are terrible and some of them are actually really good! A manager once told me they were made by the same company that makes Estee Lauder (I don't know how far I would believe that though!) There best make up products are probably their make up palettes. They are surprisingly not bad for how cheap they are.
The make up palettes are about €5/€6. They are in sturdy cases that click close. The first palette is a 36 eyeshadow palette. This product is not bad, you get 36 colours for €6! The colours vary in pigmentation but some are surprisingly good! It's perfect if you are looking for a cheap palette to throw into your bag for travel and not really care if you loose it or break it. It's also a good buy if you are new to make up and want to try out some new colours without breaking the bank.
Next up is the Glitter Eyeshadow Palette. Strangely despite it's name it's not really all that glittery. This palette is also about €5/€6. It contains 10 eye shadows about the size of a €2 euro coin. I really like this palette. Most of the eye shadows are really pigmented apart from a few of the lighter shades. They are a bit chalky but considering how cheap this would not bother me too much. Again it's perfect for throwing in a bag without worrying about breaking it.
A word of warning I would stay away from the Hello Kitty eyeshadows as they are awful. Stick to the big palettes or ask a member of staff for a tester. For bronzer lovers out there the H&M bronzer is supposed to be amazing (I don't wear bronzer so I CAN'T confirm this!) It did used to sell out within a few days of delivery with people buying 4/5 at a time to stock up! If you love your bronzer maybe check it out!