I know of Google and Bing, but are there other places I can/should submit my sitemap.xml? And do they support pinging?
Outside of signing up for the various web master tools accounts, Bing, Google, Baidu, et. al., the robots.txt file can be used to generally announce the existence of a sitemap file. You use the following example in your robots.txt file which is possibly the best way to get the various search engines (generally speaking) to use your sitemap.
Some sites have a ping utility such as Bing and Google.
I have not seen any evidence that ping for Bing (poet and don't know it) works and the Google ping assumes a web master tools account. Somehow, I think the various ping utilities have fallen out of favor over the years.
Of course, I strongly recommend signing up for webmaster tools account for Bing, Google, and possibly Baidu but Baidu seems to weird about using sitemaps. Having a web master tools account does encourage these search engines to use your sitemap. For Google, creating a Google Search page ensures that your sitemap is read and the whole site spidered immediately and very fast.