What is bitcoin core developers solution to the increasing number of transactions?
BIP 100: Jeff Garzik Miners vote on blocksize, constrained between 1 and 32 MB.
BIP 101: Gavin Andresen Blocksize increases to 8 MB, and doubles every two years after that. (This is what XT implements.)
BIP 102: Jeff Garzik Blocksize increase to 2 MB. (Intended as a fallback that everyone can agree on.)
BIP 103: Pieter Wuille Blocksize increase by 17.7% each year, consistent with current technological growth.
BIP 105: BtcDrak Each block increases or decreases blocksize by up to 10%. The change stacks multiplicatively. Voting to increase blocksize requires more proof-of-work, but not voting to decrease. The result is constrained between 1 MB and 8 MB.
BIP 106: Upal Chakraborty If more than half of last 2016 blocks are 90% full, double block size. If more than 90% are less than 50% full, halve block size.
It's a feature, not a bug: Almost-full blocks will encourage people to raise their fees, increasing the reward for miners, and thus increasing the amount of hashpower applied to Bitcoin.