Both the Xbox One and PlayStation 4 aren't backwards compatible. Sony has worked on a solution however, to at least offer legacy games from their previous systems through the streaming service, Gaikai. Through Gaikai, players will be able to access a library of PS1, PS2 and PS3 games on the PS4.
The service however isn't coming with the launch of the PS4, instead, it will be available in North America, sometime early 2014. However, things aren't looking so good for the European regions.
CEO of SCEE, Jim Ryan, has stated that the date for Europe hasn't been ironed out due to "bumbs along the road that need to be ironed out." In an interview with Edge, Jim stated the following:
"The plan is to begin with North America next year and the plan is to provide a streaming service that will allow for PS3 content initially to be streamed to firstly PS4 then PS Vita and then PS3, and so that will happen in 2014 in North America initially. Now, and I touched upon these issues of broadband in Europe during the presentation - Europe is of course on the roadmap for that service to be deployed at some point in the future, but for reasons outside of our control we don't yet have a timeline for it,"
It's highly improbable that Sony would cut out Gaikai's service from Europe entirely, without some kind of work around, however it does seem that the European market will have to wait a bit longer before it is implemented.