As far as I understand a Network
Switch handles traffic "intelligently"
in the way that it only propagates
packets to its port where it knows
that the receiver is located (In
contrast to Hub which brute force
sends all data to all ports).
Yes, that is correct.
So a Switch needs to remember all
adresses of Hosts connected to it. If
the host is not found the packet is
sent to the default route (commonly Up
link to a wider network)
Well, not quite. It's true that a switch remembers which hosts are connected to which port (usually by observing the MAC addresses of the packets arriving on the ports). However a switch normally does not know about the "default route", as that is a concept from a higher networking layer. Switches work on layer 2 of the OSI model (data linke layer). The "default route" is a concept used for routing, which happens at layer 3 (network layer).
A switch therefore does not have a "default route". If it does not know a destination MAC address, it just sends the packet to all ports (at least at the beginning, that's all it can do - this is known as "flooding"). At any rate, in an ethernet, each packet must be addressed to a local MAC address, otherwise it'll never arrive. Packets sent "out to the internet" still get a local MAC address destination, namely the address of the network's default gateway. The switch just passes this packet on to the default gateway, and the gateway (which operates at layer 3) then reads the "real" destination from the IP address embedded in the packet and sends it on its way.
Does a Switch remember IP-Addresses or MAC-Addresses to
calculate its decisions?
As explained above, a switch is IP-agnostic, as it works on a lower level of abstraction. Thus, only MAC-addresses.
One complication: As explained in wolfgangsz's answer, there are switches which also operate on layer 3 (so-called multilayer switches). These are a bit more complicated, and they can handle IP addresses and more.