When we first started we used one account for all our clients. As we reached the campaign limit on the account we'd just set up a new one.
It made setting things up faster because we didn't have to walk our sometimes technical dinosaur clients through the process of logging into an AdWords account and entering their card details for payment. We paid all the Google charges and recovered them from the clients.
That was before the days of the MCC account.
There were some problems with this approach.
These days we use an MCC account with one separate AdWords account per client. I recommend you do this if you plan on taking on more AdWords clients.