I'm looking for a piece of hardware to connect to different types of ISPs, normal DSL, cable DSL and USB egde sturfstick to offer one Internet connection with a higher cumulated bandwidth. I'm pretty sure something like this exists, but I don't know how to call it or where I can find something like that.
It is link aggregation and one of the more popular technologies to achieve this at the carrier and higher-end networking level is via MLPPP (Multi-Link Point-to-Point Protocol).
Something like the Peplink Pepwave Max Mobile Router would accomplish what you're looking for.
http://www.peplink.com/max-mobile-router/
That's called link aggregation, but with the added complexity of differing media types. Hope this helps in some manner.
If you want a cheap router to do it, you can buy a DD-WRT compatible one (I'm running an ASUS RT-N16 in the office, it's great!) and config it yourself
http://www.dd-wrt.com/wiki/index.php/Dual-WAN_for_simple_round-robin_load_equalization