I don't really mind Flash that much. It's a lot like Java, though; I don't mind it if I know that I'm going to a page with a Flash or Java object on it. What I do mind are when Flash and Java objects appear in pages in completely unnecessary ways. Like I mentioned before, intros and menus that use Flash are bloody stupid and generally just pointless. Sites built using Flash are also plagued by numerous problems. For one, it's an accessibility nightmare. Anyone using a screen reader, navigating by keyboard, or dumb enough to expect things to run smoothly and in a sane, standard way are all screwed. They also foil any attempts to link to a certain page, not to mention eliminate the possibility of doing a simple copy-and-paste operation most of the time, as well as make printing virtually impossible. Let's not forget that while your monitor may be running at a high resolution -- say 1600x1200 -- you're still stuck in the Flash object's tiny window. A lot of detection methods are also horribly broken, breaking the page on Firefox, IE, Opera at best, breaking them on Linux, OS X, or portable Flash-powered devices at worst.
Java is pretty good, though, probably the most mature cross-platform interpreted language in existence (I still say that .NET would be very good competition if Microsoft provided more resources to the Mono project, but that's neither here nor there). The biggest problem that I have with Java is how long it takes to start up the bytecode interpreter. Flash objects typically take a second, tops, while Java applets take five or more seconds to start up. It's not a whole lot of time, but still, having your browser freeze up for seconds at a time on a fairly quick system is annoying. It's fine after that, thankfully.