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And SublimeCodeIntel does intelligent autocomplete for: PHP, Python, RHTML, JavaScript, Smarty, Mason, Node.js, XBL, Tcl, HTML, HTML5, TemplateToolkit, XUL, Django, Perl, Ruby, Python3.

Not quite at the level of an object/class browser like Visual Studio, but it does provide for some key functionality in this area.

While you're at it, check out SublimeLinter too.
Check out the SublimeCodeIntel plugin, which does a quite nice job of meeting this goal, in addition to being syntax-aware for many programming languages.

Note if you have install issues, be sure to try restarting Sublime at the point of failure; that's what got it to install properly for me.
I have recently discovered the SublimeCodeIntel plugin which provides a basic level of project indexing, project-wide auto completion, and "goto declaration" functionality. Works great.

I also highly recommend the SublimeLinter plugin which provides realtime code error analysis like many of the full fledged IDEs.
I see this also at smaller font sizes, but not larger ones. Perhaps it is just a rounding/off-by-one error.
It seems that if you View->Hide Menu while in Distraction Free mode, it will remember this setting between sessions, and keep the menu hidden -- specifically in Distraction Free mode only.
Thanks for the tip.

I have also found the SublimeCodeIntel plugin to do this and more.
For consistency it might make more sense to call it "auto_complete_commit_triggers" and conform it to the same values pattern that "auto_complete_triggers" already uses. I would think that we could just put different values for "auto_complete_commit_trigger_characters" in <filetype>.sublime-settings files equally as well though.
I think I would like this if we still retained the ability to create an unnamed file quickly with e.g. Ctrl-N -- mainly for when I want to take a quick note or paste some chunk of text in and do some one-off manipulations to it without ever saving.
I can confirm this works. I kept my work and home Sublime Text 2 folders synchronized using Dropbox and an NTFS junction as described in the above link.