I would like to go swimming.

[Arctica1982]

Hello!

I would like to go swimming. As far as I know, this is the correct form.

What about this:

I would like to swim.

 

[emsr2d2]

Both sentences are grammatically correct. The first is more common and natural.

 

[Tdol]

There are contexts where the second would be fine - I would like to swim the English Channel - but without the extra context, it isn't particularly natural.