The connector industry term for two PCB's connecting end-to-end is co-planar mating. I declare an interest as I work for GCT.
If you're using standard, 'post and box' connectors, which are the most economical choice there is one key issue to watch out for - the mating centreline of the connector should be at the perfect height, IE exactly the same for header and socket. I've had lots of experience designing in these connectors with customers, and often manufacturers datasheets don't list the appropriate information, this is because these connectors often mate with multiple ranges and are not specifically for co-planar mating. Just choosing a right angle header and socket with the same contact pitch is not always enough!
You'll find many connectors targeted at LED lighting on the market, these are normally used to connect thin and long LED strips in end-to-end fashion, however they tend to be single row and a limited number of circuits (less than 6), which doesn't suit all applications, I notice the original question was for 10 circuit!
You can choose numerous options, as thru hole is covered in another answer I've suggested some SMT options below:
2.44mm (.1") pitch SMT -
Female - http://gct.co/connector/?series=BG230
Male - http://gct.co/connector/?series=BG080
2.00mm (.079") pitch SMT-
Female - http://gct.co/connector/?series=BF088
Male - http://gct.co/connector/?series=BF035 (BF036 for with locating peg).
1.00mm (.039") pitch SMT- tiny option upto 40 contacts
Female - http://gct.co/connector/?series=BC075
Male - http://gct.co/connector/?series=BC034