Sadly, not everyone submitting your forms will be a human being. Whatever is open for (human) interaction will also be accessible to bots, who are and will remain highly capable of simulating real interaction and continue to be a nuisance.
But it really isn't too hard to fend off generic spam attacks. It all boils down to making things hard enough for spammers by adding some hurdles that make it unlikely enough for bots to make it past.
At some point, it simply is no longer worth a spammer's time and effort to implement more sophistication to get past your barriers. After all, just the simple fact that you're investing into warding them off is a clear indicator that you're not a gullible audience for their spam: even if their spam would make it past your layers of protection, you still wouldn't be likely to interact with their message, and their efforts would've been for naught anyway.
While there's no silver bullet against spam bots, it's easy enough to make it inconvenient enough for spammers to bother.
Here are a couple of techniques for mitigating spam, in order of personal preference: (is that even a word? Probably not)
We're done for real now; let's start receiving emails!