So it could be any kind of bag really and admittedly I'm borrowing a bit from March's 'gift of the month', but Aly Bond recently made this beautiful clutch bag for a friend at a very reasonable price, so I was keen to put this forward in it's own right as a gift idea. 
A group of us wanted to give our friend a personalised and individual gift to celebrate her 40th birthday recently. Each of us put a little message and/or picture on a square piece of cotton using fabric pens and then took them to Aly with a broad idea on what we wanted them sewn into. She then gave more specific suggestions and once agreed, made a lovely clutch bag using leather she supplied (she reuses a wide variety and colour-range of off-cuts and recycled pieces from various suppliers) and the fabric squares we'd given to her within the lining. 
It was a really effective and professional finished piece which we then presented with gift vouchers inside...