Flash memory does have a limited number of read/write cycles, but to what degree I am not sure. I am sure though that the current generation of flash technology is better than its predecessors, as I believe with early flash models you could only read/write a couple thousand times or so. That's great for storage, however not so good for constant the read/writes you see with hard drives.
Read cycles are unlimited.
Write cycles effectively are too.
It's the less-than-obvious
erase cycles that limit the lifetime of Flash. Flash's natural state is to be all binary 1's.
Transitioning any collection of bits within a single Flash page (think hard drive "sector") from 1's to 0's involves selectively "writing" to that page.
If you want to transition any collection of bits in a page from 0's back to 1's, then you have to erase the whole page back to 1's all at once, and start over from scratch.
You can expect lifetimes in the order of 100,000 erase cycles from most Flash today. That's 100,000 erase cycles per page. If you make sure to leave plenty of free space in the Flash, then an intelligent Flash controller will automatically use wear-levelling techniques to redirect the mapping of logical pages around amongst all of the available physical pages, thus spreading the erase cycles around so that it can effectively increase the Flash's overall lifetime significantly.
For example, assume you're using Flash with a 1 kilobyte physical page size, and you always keep 3 gigabytes of free space. The Flash controller will have approximately 3 million physical pages to choose from as it wear-levels the modification of logical pages. That works out to over 300 trillion erase cycles before you'd statistically expect the drive to start being in imminent danger of wearing out. At those numbers, you're probably looking at an expected lifetime in the order of years to decades, depending on usage patterns.
Flash that's used to house a heavily used paging file/swap partition (AKA what most people are talking about when they use the phrase "Flash RAM") will wear out much more quickly that Flash that's used to store programs and documents.