I don't recall any event involving a 737 this year, but there was a 767 that had gear issue towards the end of 2008. In that particular instance, I think the issue was that the hydraulic jack on one of the nose gear doors had come adrift, and the door was basically flapping in the breeze. It was talked up by the media at the tiime, but really fell into the non event category.
In a Boeing, assuming you have all of the hydraulics working properly, about the only reason I can think of for all of the gear not retracting would be that the gear pins are still inserted....which means you did a pretty poor preflight. Individual wheels, or doors, can be affected by lots of issues. Remember that we consider the doors not closing properly to be the same as the gear not retracting...it imposes the same limits. In an Airbus, because the gear handle is simply an electrical switch, with no mechanical connection to the gear system, a complete failure to retract would most likely be something to do with that switch. Of course the gear not retracting is rather less of an issue than the opposite.
Could you continue? Well, yes and no. Certainly, the aircraft can be flow for an extended distance with the gear down. But, the fuel burn will be dramatically higher. You will cruise much lower (about half the normal height), and you will be severely speed limited. All of that adds up to something rather nasty...you'd be unlikely to have enough fuel to be able to complete the trip. If memory serves correctly, somebody tried that in an A310 in Europe, and ended up duplicating the Ghimli glider.
