Google Chrome Application for Android
The Google Chrome Application for Android comes with some sync features as to allow users to keep their web-experience mirrored to other devices or desktop computers.
You need to be signed in on the services screen:
If you're not on the sign-in services screen, touch Menu > Settings > your email address to manage your sign-in options.
You can adjust your sync settings from the Services screen:
touch Sync to adjust your settings.
You can either set the sync to affect all data or specify each data is intend to be synced:
Note:
To fully take advantage of this feature, make sure you're signed in to Chrome on other devices, such as your computer or tablet.
Additional documentation about this can be found at Google Chrome Support page for sync data.
Google Web History
Google takes care of this for you as long as you've logged yourself into your Google Account on every browser and/or device you use.
Additionally, using history.google.com, you can manage the information stored:

What I most enjoy with this is the fact that all my searches are synced between Mobile, Desktop and Laptop, saving me precious time.