I've always used Nginx as a proxy, but I've seen HAProxy mentioned, what are some of the benefits of using HAProxy over nginx as a proxy or load balancer?
Multi-tenant hosting for customers with lots of custom domains (with SSL) with different customers on different versions, and an app with lots of legacy. In older versions, different paths are handled by different servers. Some paths use source-ip sticky. One part of the app uses websockets. Some paths are handled via S3+cache layer (offloading traffic from app servers without changing the app).
There's also a bunch of special paths to access specific servers directly to get some health metrics (from app written without thinking about running in an auto-scaling environment). One fun thing I built handles some old SOAP requests from a defunct service running on hundreds (maybe down to dozens now?) of external systems that will retry every request forever (exponential traffic growth) if they don't get a "success" response; using Haproxy and some request capture regexes, it can return one of a dozen specially crafted hard coded "success" responses. The date is wrong but the service doesn't care, and now few lines in Haproxy replace a dedicated "black hole" app server we used to run.
Haproxy handles all this in a single hop for all traffic (and Haproxy itself runs in an autoscaling group). The config is complex, but still understandable. All the variable stuff is generated by scripts at runtime, which also lets us use an admin UI to manage customer domains, versions, and automatically picks up available (deployed) application versions in the region.
Having used both, I'd say in general nginx is easier for simple things, and in many ways has more capabilities (like static hosting, authentication support). In fact we use nginx on the Haproxy servers for hosting static pages and being a caching proxy for S3. Haproxy makes simple hosting more complicated, but you get a lot of very fine-grinned control over everything (eg, it's pretty easy to do almost anything to the traffic like changing request/response headers/paths at any point). For anything new, I'd use nginx only if I could get away with it (note: all the above may be possible in nginx now, but I'm not going to rewrite our infrastructure unless there's a very good reason).