All of them, BUT some of those things do have an associated cost.
Deleting Temp Internet Files -- which only applies to IE, which is not the wisest choice of browsers for various security related reasons --- will save a little disk space at the expense of making web browsing slower. If you take an average page from these forums, even though the pages are generated on demand, there are still several elements which the browser will store local copies of. Like the Cnet logo image at the top, all the little icons in the legend thing at the bottom, the newsletter image... So rather than having to download those again, the browser just pulls up the local copy, speeding up the overall page loading process.
DNS cache is along the same lines. If you go to a site a lot, like say google.com, it will keep the IP address google.com points to, so it doesn't need to go ask a DNS server to look it up for you. The only time you want to clear your DNS cache is if an entry seems stale. Meaning you're having trouble accessing a site, and you know (from asking others) that the site is working. It won't HURT anything, but it will have a small negative effect on your web browsing.
Log files and memory dumps can be useful in figuring out what went wrong if a program or the OS crashes. They're not strictly necessary, but are generally there for a reason.
The clipboard is generally stored in memory, so that one sounds particularly useless, but it certainly won't hurt anything to get rid of whatever may be there.
The Check Disk fragments are typically useless, but if you really know what you're doing, can potentially help you reconstruct a file that had the misfortune of becoming corrupted or damaged. Of course if you find that the program seems to be deleting a lot of these, then you probably have other issues, up to a failing HDD and/or bad RAM.
Cached fonts, are like anything else cached. It's done to speed things up. IIRC, this is used for font menus where they show a live preview of what the font looks like by writing the font name in the font. So the system can just store that, rather than have to go read each font file you have installed, get the characters needed from it, and then fill out the drop down box. That's why it might be slow the first time you go to pick a font in MS Word, but every subsequent time it's almost instantaneous. Because the system cached the results.
Start menu and desktop shortcuts again won't hurt anything, but might impede easy access to certain programs.
All too many people think of programs like CCleaner (or Cocktail and Onyx on the Mac side of things) as a panacea sort of program. Or this magic performance enhancer that reminds me of those male anatomy enlarging pills spammers are trying to scam people with constantly, since each one is about as effective at doing what the gullible user thinks it will. CCleaner is really intended to be more of a surgical strike kind of program, able to go in and target the specific areas needed, not a carpet bomb where you just kind of obliterate anything in the general area. And honestly, how much effort is it really to empty the recycle bin manually? It can't be any more effort than launching CCleaner and telling it to perform some action. And you shouldn't be using Internet Explorer if you don't like malware infestations anyway, so there shouldn't be anything in the TIF area to delete, but even if you foolishly continue using IE, the TIF cache is limited to a set size, and it will automatically start deleting files to make room for new ones when it reaches that limit. So, you might gain some disks space back after clearing that out, but any web browsing you do will just cause IE to start filling it back up.
My advice, is to just eschew all of these programs that claim to improve performance or maintain Windows in some way. Truth is, Windows doesn't really NEED much in the way of maintaining, what it needs is for users to keep out of its way with programs like CCleaner, registry fixers/cleaners, and all of those various "tweak" programs. If you avoid using Internet Explorer then your risk of malware infection drops significantly, and you can blissfully use Windows for months, even years, at a time without ever having to lift a finger maintenance wise.