LTE: The theoretical max is 300Mbps DL and 100Mbps UL in 20MHz spectrum. Some documents show upto 350Mbps but lets just assume 300Mbps as its reasonable high. In practice, getting a 20MHz contiguous band may be difficult in most parts of the world. Also, the practical rates would be far lower due to interference and large number of users.
Lte-Advanced: The main feature in LTE-Advanced related to general speed is Carrier-Aggregation that allows the operator and LTE-A capable device to aggregate upto 5 20MHz bands, so in theory the max. speeds would be 1.5Gbps (300Mbps x 5) DL and 500Mbps UL. As you can guess, in practice this may be impossible but nevertheless its a good figure to have.
