Flash RAM cells in SSDs have a limited lifespan. Every write (but not read) cycle (or more accurately every erasure) wears a memory cell, and at some point it will stop working.
The amount of erase cycles a cell can survive is highly variable, and flash from modern SSDs will survive many more than flash from SSDs made several years ago. Additionally, the SSD intelligent firmware will ensure evenly distributed erasures between all the cells. In most drives, unused areas will also be available to backup damaged cells and to delay aging.
To have a value we can use to compare the endurance of a SSD, we can use lifespan measures such as the JEDEC published standards. A widely available value for endurance is TBW (TeraBytes Written, or alternatively total bytes written) which is the amount of bytes writeable before the drive fails. Modern SSDs can score as low as 20 TB for a consumer product but can score over 20,000 TB in an enterprise-level SSD.
Having said that, both the lifespan and the use of a SSD for swapping depends on several factors...
Systems with plenty of RAM
On a system with plenty of RAM and few memory consuming applications we will almost never swap. It is merely a safety measure to prevent data loss in case an application ate up all our RAM. In this case, the wearing of a SSD from swapping will not be an issue. However, having this mostly-unused swap partition on a conventional hard drive will not lead to any performance drop, so we can safely put our swap partition (or file) on that significantly cheaper hard drive and use the space on our SSD for something more useful.
Systems with little RAM
Things are different on a system where RAM is sparse and cannot be upgraded. In this case, swapping may indeed occur more often, especially when we run memory-intensive applications. In these systems, a swap partition or file on a SSD may lead to a dramatic performance improvement at the cost of a somewhat shorter SSD lifespan. This decreased lifespan may, however, still not be short enough to warrant concern. In all likelihood, the SSD may be replaced long before it would've died because several times the storage may be available at a fraction of today's prices.
Hibernating our system
Waking from hibernation is indeed very fast from a SSD. If we're lucky and our system survives a hibernation without issues, we can consider using an SSD for that. It will wear the SSD more than just booting from it would, but we may feel it's worth it.
But booting from an SSD may not take much longer than waking from hibernation from an SSD, and it will wear the SSD far less. Personally, I don't hibernate my system at all - I suspend to RAM or quickly boot from my SSD.
The SSD is the only drive we have
We don't really have a choice in this case. We don't want to run without a swap, so we have to put it on the SSD. We may, however, want to have a smaller swap file or partition if we don't plan to hibernate our system at any point.
Note on speed
SSDs are best at quickly accessing and reading many small files and are superior to conventional hard drives for transferring data from sequentially-read small or medium-sized files. A fast conventional hard drive may still perform better than an SSD at writing (and to a lesser extent reading) large audio or video streams or other long unfragmented files. Older SSDs may have their performance decline over time or after they are fairly full.