Trading clipboard contents between phone and computer
If all you care about is the clipboard sharing, you might want to take a look at ClipSync. This app allows you to share your clipboard between multiple Android devices and your Windows PC: Copy on one device, and it appears in the clipboard of all others. At least that's what the app description says (all Windows I have are just for fresh air and light coming in, or to look out of them (not Out-look), so I cannot verify). A 4.5 star rating suggests it works -- and it's only 150kB "big".

If you want a bigger benefit, take Compro01's advice and have a look at Airdroid. It's a great app, and lets you maintain your Android device from any web browser in the same WiFi network really nice (edit your contacts, write SMS, browse pics...). An beside that, allows for clipboard sharing.