"Cactus" has an unusual plural form: "cacti". There the best way to say it is: **A cactus has a lot of spikes.** You can also say: "Cacti have a lot of spikes", and that would be correct, too, but the singular sounds better.

Cacti have a lot of spikes. More technically accurate would be to say: Cacti have a lot of spines.

Maybe.... The plural for "cactus" can be either "cacti," "cactuses," or "cactus," depending on where you are and who you talk to. So, you could say your sentence, but more often, you might also hear "Cacti have a lot of spikes" or "Cactuses have a lot of spikes."