The quick answer to this is no but there is more to it than that. Spin bikes or indoor cycles are designed to be like outdoor cycles.
Just like those cycles you can ride the indoor variety without specialist shoes.
Most spin bikes come in 2 types when it comes to pedals. They either fit standard shoes or they have dual pedals with one side for ordinary shoes the other for specialist shoes. You can also, for most bikes, change the pedals over for your own as most use a standard thread of 9/16″, which is the same as outdoor bikes.
The pedals that fit ordinary shoes normally have cups and straps to fix and hold them in place. The best shoes are flat like athletic or cross-trainers rather than running shoes with the raised soles. They fit better into the straps and get a better grip on the pedals. The best shoes will have a stiff sole, keep your foot in place, have a breathable upper and made of durable materials. This gives you more force on the pedals, they keep your feet from tiring out, and the breathable upper helps to get air circulating keeping your feet cooler.
These do give you a good solid grip on the pedals for strong pedal strokes but they don’t give the same grip or efficiency as you’d get with a specialist shoe.
What Specialist Shoes
Most bikes that have pedals that fit specialist shoes are SPD. These are where you’ve have cleats on the bottom of your shoe that clips on to the pedal.
Shoes with a recessed cleat with a rubberized sole are the best to prevent accidents while walking around on the floor and not damaging the floor.
The best source for SPD cleats and shoes are from bike shops or online. They can take a little time getting used to at first but once you do you may want to keep them. You need to figure out how to clip in and out and use them to push and pull to give a better grip the whole way round.
The bikes at the more affordable end of the scale tend to come with just the standard pedal with toe baskets and straps (Sunny Health And Fitness Pro Indoor Cycle). It’s not until you get to the mid-price range where you find dual pedals with SPD on one side and toe baskets on the other side (See Sole SB900) and at the upper end they tend to come as standard (see Keiser M3 Plus and Spinner NXT).
There are some bikes that fit the Look cleats which protrude like the Look Delta shoe. These can make walking around difficult , they can be slippery and may damage your floor. (But most don’t)
It is possible, if you want, to fit your own pedals to most spin bikes including the lower priced ones. They can range in price from $30 – to $100 and beyond. The shoes themselves also have a similar price range. In addition you need to buy cleats that are around $10 to $15 for a set.
Benefits Of specialist Shoes
You don’t need the specialist shoes but you do get a better ride and they can help with more efficient pedaling stroke. You use your quads and hamstrings more effectively as well as calves and shin muscles. This all helps for better stability of the legs and feet helping to prevent foot numbness that can sometimes occur and is more prevalent when athletic shoes are used with toe cages. The balancing up of the muscles in this way can also help with the aesthetics so that none of the muscles appear over or under developed in comparison with each other.
It is a more balanced stroke over all for your foot, promoting a more fluid stroke through the down/upward parts of the stroke.
They also help in positioning the foot correctly on the pedal with the ball of the foot being clipped in place on the middle of the pedal. Your climbs due to this stability are going to be stronger.
With a toe cage the temptation is to push your foot right to the end of the cage and strap into place. this can result in your foot being too far forward which will cause your foot to arch and to go numb or go to sleep.
So, as I said at the beginning you don’t need specialist shoes with cleats to use a spin bike as the pedals either are just for athletic shoes or are dual to use for cleats and ordinary shoes.
If you are only going to use the bike for moderate exercise or casually then you are likely to be okay with tennis shoes. But as you become more serious and increase intensity and length of your workouts you are going to appreciate more and more the benefits that come from wearing specialist shoes.