Recs.
Updated
SpecsUpdate
Pros
Pro Free tier
While IRCCloud is generally a subscription service, a limited free tier is available. It's limited to 2 external IRC networks besides irc.irccloud.com, accounts get disconnected after 2h while no frontend is used (does not apply for the first 7 days) and 100MB file sharing limit as well as it lacks a number of team and enterprise oriented features.
Pro BNC by default
All other irc clients are only connected to the network as long as you are online. IRCCloud provides a bouncer by default, i.e. an irc proxy that maintains your presence and logs all chat. Said BNC remains online for 3 hours by default, papering over connectivity losses, or for a small fee of 4€ per month, you can remain online forever (good for travels and such).
Pro Prototype web wrapper client
There is a primitive, but consistently updated web wrapper that can act as a desktop client available on github. They don't exactly publicize it, but it is being actively developed all the same. It will likely evolve into a full-featured dedicated desktop client in time.