I can't see much that you can/should get rid of:
Trusteer = Security software which many banks insist that you have on your computer if you're using internet banking. [Keep unless you don't use internet banking]
Synaptics = Driver for your touchpad [Keep]
Realtek = Driver for your soundcard (or onboard sound) [Keep]
Quicktime = A media player sometimes used to show animations or videos on websites designed ages ago but generally useless [I'd ditch it but make sure that I'd got a decent media player, such as VLC or GOM, instead].
OpenOffice = Your office software suite [Keep unless you've got an alternative, which you prefer, available to you]
Olympus Camedia = Elderly graphics application, supplied with Olympus cameras about a decade ago. [Keep if you actually use it and like it; otherwise remove it. There are lots of better free image-processing programs available these days - ask if you need advice about choosing one]
Mozilla entries - Related to your Firefox browser [Keep unless you never use Firefox].
Microsoft Visual C+ entries - Related to software called on by other programs based upon that type of programming [Keep]
Microsoft Security Essentials = Your security software [Keep unless you plan on replacing it with something else, such as Avast]
Microsoft Office entries - Relate to the 'Enterprise' version of Microsoft Office, which was possibly a trial version supplied with your laptop (requiring you to purchase a key to keep it working) [If you don't use Microsoft Office, which would seem to be likely as you've got OpenOffice installed, you can remove those entries]
Microsoft.NET = A program called on by other programs, which require its presence [Keep]
Malwarebytes = Your anti-malware program [Keep]
HP Update = (I think) a customised version of the Windows updater [Keep]
HP Photo Creations = Software for designing greetings cards, calendars, etc [Keep if you actually use it; otherwise consider getting rid of it]
HP FWUpdateEDO2 = Software for linking together the functions of your HP printer and checking for updated versions of drivers, etc. [Keep unless you've no longer got an HP printer]
HP Deskjet 3520 Entries - All relate to that printer [Keep as long as you've still got the printer]
Defraggler = A better disc defragmenting program than the one that's to found within Windows' accessories [Probably keep but W7 defrags itself as you go anyway, so you shouldn't need to run any defrag program normally]
CCleaner = A registry cleaner. [Keep but use with caution. Ensure you understand what changes it will make before using any of its functions]
Bing Bar = A toolbar for Internet Explorer [I'm not a great fan of adding on toolbars to browser but, if you use Internet Explorer and like having the Bing toolbar there, keep it. However if you only use Firefox you might as well get rid of it]
ATI Catalyst = Driver (etc) for your video card [Keep]
Adobe Reader = Your PDF viewer [You need a PDF viewer but Adobe Reader is clunky and resource-hungry. I'd recommend getting rid of it and replacing it with either SumatraPDF or Foxit. However you could simply keep it if you want to]
Adobe Flash Player = Software required by some websites in order for them to be able to display video files [Keep but go to the Adobe website to check that it's up to date; older versions present security risks]