Multiplexed 1 Gbps Ethernet?
Yes, it's called a variety of things such as 'teaming', 'etherchannel', 'DMP', 'MPIO', 'bonding' etc. but it happens all the time and is supported by most modern operating systems straight out of the box.
It's a very advisable thing to do if you have the spare ports on the server/pc and the switch - firstly because it allows you machine to carry on if a port or cable breaks and secondly because they can in many circumstances aggregate your traffic down both links to effectively give you 2Gbps.
Feel free to ask any more detailed questions around this area.
So-called 'smart switches' employ a thing called Link Aggregation Control Protocol which allows you to bundle multiple ports together and use them as if they were one wide link... I'm not completely clear as to your precise need, but this maybe another term worth researching.
Switches usually support some (~64) aggregated links with up to 8 ports each. But before adding a Quad-NIC to a single server you should think putting about a load balancer with 4 GigE ports in front of your servers.
When using LACP, it's important to know which load balancing algorithm is used by the trunk. Normally you can (and should) choose between MAC- and/or IP-addresses and/or TCP/UDP-Ports as a source for load balancing.
Failover is really fast with LACP, you lose just a little more than the packets on the wire.