Need free form hosting? You'll love Bitrix24. Most free popular hosted form providers severely restrict how many submissions you can receive each month without paying. 100-1000/mo cap is typical. Another popular restriction for free form hosting services is limiting the number of employees who can access forms to one (12 free users in Bitrix24). But most importantly, each form in Bitrix24 has both a public page and embed code. This means that you don't need a website to host form, but if you do get one later on, you can embed all your existing forms there without any service interruptions. In fact, you can use both (site embed and public Bitrix24 form page) at the same time.
Bitrix24 CRM manual is available here.
If you are interested in buying self-hosted editions of Bitrix24, which come with API, CMS and source code, can be easily customized and integrated with other tools, please download a trial version here.