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It sounds like you may have accidentally enabled Transform Snapping (⇧ Shift↹ Tab).

By default transform snapping will snap objects to fixed increments as they are being transformed.

Transform snapping:
The ability to snap Objects and Mesh element to various types of scene elements during a transformation is available by toggling the magnet icon (which will turn red) in the 3D view's header buttons.

Increment:
Snap to grid points. When in Orthographic view, the snapping increment changes depending on zoom level.

You can disable it by clicking the magnet icon in 3D view > Header, or by pressing Shift+Tab:

It sounds like you may have accidentally enabled Transform Snapping (⇧ Shift↹ Tab).

By default transform snapping will snap objects to fixed increments as they are being transformed.

Transform snapping:
The ability to snap Objects and Mesh element to various types of scene elements during a transformation is available by toggling the magnet icon (which will turn red) in the 3D view's header buttons.

Increment:
Snap to grid points. When in Orthographic view, the snapping increment changes depending on zoom level.

You can disable it by clicking the magnet icon in 3D view > Header, or by pressing Shift+Tab:

Enabled Disabled

For Version 2.8.

It sounds like you may have accidentally enabled Transform Snapping (⇧ Shift↹ Tab).

By default transform snapping will snap objects to fixed increments as they are being transformed.

Transform snapping:
The ability to snap Objects and Mesh element to various types of scene elements during a transformation is available by toggling the magnet icon (which will turn red) in the 3D view's header buttons.

Increment:
Snap to grid points. When in Orthographic view, the snapping increment changes depending on zoom level.

You can disable it by clicking the magnet icon in 3D view > Header, or by pressing Shift+Tab:

It sounds like you may have accidentally enabled Transform Snapping (⇧ Shift↹ Tab).

By default transform snapping will snap objects to fixed increments as they are being transformed.

Transform snapping:
The ability to snap Objects and Mesh element to various types of scene elements during a transformation is available by toggling the magnet icon (which will turn red) in the 3D view's header buttons.

Increment:
Snap to grid points. When in Orthographic view, the snapping increment changes depending on zoom level.

You can disable it by clicking the magnet icon in 3D view > Header, or by pressing Shift+Tab:

It sounds like you may have accidentally enabled Transform Snapping.

Transform snapping by default will snap objects to fixed increments as they are being transformed.

Transform snapping:
The ability to snap Objects and Mesh element to various types of scene elements during a transformation is available by toggling the magnet icon (which will turn red) in the 3D view's header buttons.

Increment:
Snap to grid points. When in Orthographic view, the snapping increment changes depending on zoom level.

You can disable it by clicking the magnet icon in 3D view > Header, or by pressing Shift+Tab:

It sounds like you may have accidentally enabled Transform Snapping (⇧ Shift↹ Tab).

By default transform snapping will snap objects to fixed increments as they are being transformed.

Transform snapping:
The ability to snap Objects and Mesh element to various types of scene elements during a transformation is available by toggling the magnet icon (which will turn red) in the 3D view's header buttons.

Increment:
Snap to grid points. When in Orthographic view, the snapping increment changes depending on zoom level.

You can disable it by clicking the magnet icon in 3D view > Header, or by pressing Shift+Tab: