I fancy trying speedplays. Currently I use SPD SL on my road bike. Do I need to get new shoes?
Without knowing what your existing shoes are, by the very nature you currently use SPD-SL then you'll be fine.
I went from Speedplay Stainless to SPD-SL with my existing shoes and boots, so just the same as you want to do only in reverse.
Speedplay are fantastic pedals and given the choice I'd only ever use them TBH. I only changed back to SPD-SL when I had 2 bikes, and truth be told I couldn't afford to fit Speedplays on the 2nd bike, so as I wanted one pedal type so my shoes nad boots had the same cleats I went back to SPD-SL.
The only gripes with Speedplay are the stack height is a real issue if you want to walk in them, you can get cafe covers but they only protect the cleat, they don't really make walking easier apart from offering more grip, and as the retaining mechanism is built into the cleat replacement cleats are expensive compared to SPD-SL and others.
If you can live with the poor walking, (even worse than SPD-SL), and the cleat cost then go for it, they are brilliant.
In fact as I'm back to one bike I might sell my Dura Ace SPD-SL's and get back to Speedplay
