It completely depends on the user's settings. You can choose to allow titles to be read out, or alt text to be read out. You have no guarantee that titles will be read out.
In general you wouldn't want to have titles on anchors unless the anchor text is really short and uninformative (which one should avoid when possible). You certainly wouldn't want title text that repeats the anchor text, nor title text that states the obvious like "link1". Annoying to everyone involved.
Want to know what a screen reader reads out? Test in one. JAWS for Windows has a free 40 minute demo you can download to a thumb drive (Freedom Scientific doesn't want this to be used by developers but, oh well). There's a similar one for Window-Eyes: these are the 2 largest (most popular) commercial readers for Windows. NVDA is an excellent free one but they seem to update it much better than the Big 2.
Orca is a screen reader that comes with Linux distributions running the Gnome desktop (so, not KDE). Unlike the three Windows readers mentioned above, Orca does not have a virtual buffer (a copy of the page the user then interacts with using special commands).
VoiceOver comes with all versions of OSX, including what's on iWhatevers.
While stuff like FireVox are interesting, I'd rather test in a real reader, just as I'd rather test real browsers than browser simulators. But, you could get an idea what various readers do in various situations by checking some accessibility blogs regularly (this is easier on a developer than having a copy of every screen reader and learning how to use them all anyway).
http://www.accessibleculture.org/research/html5-aria/ (example page) has given me some excellent information
Marco's blog in general is useful... I have many of his pages bookmarked. Example page:
WebAIM often expains how the Big 2 for Windows work with various code constructs: http://webaim.org/articles/
RNIB has some articles like this one: http://www.rnib.org.uk/professionals/webaccessibility/wacblog/Lists/Posts/Post.aspx?List=be9c76d3-7ad0-4e03-a1a0-e6f6953b8178&ID=40
(yes finally they've brought that one back from the dead!)
http://www.paciellogroup.com/blog/ has general accessibility stuff which ends up having a lot of screen reader stuff
Lots of older articles about older versions of readers at JuicyStudio.com though Gez seems to not update it very much any more.
So reading about screen readers and tests that others do is useful simply because it's difficult to test them all, but I still recommend at least going through your pages with at least one popular reader. Then you can see what kinds of options the user have (mostly assume newbies will leave all reader and browser settings to default and may TAB through your pages, while experienced users will have things turned on and off and for example won't need skip links and that sort of thing).