By virtue of the same chemistry that gives titanium its unparalleled hypo-allergenic rating, the metal and its colorful oxide coating are immune to time (won't fade) and any chemical that won't send one to an emergency room.
But oil and dirt can temporarily dull some of the colors. The bronze and darker blues are most noticeably affected by greasy fingerprints and such.
Also, abrasives can gradually wear away the surface coloring. It is more durable than the colors on niobium, but it would be wise to protect your titanium from scratches. Don't store your titanium artwork loose in a drawer where it may frequently rub against other items.
To clean: Use rubbing alcohol, acetone, window cleaner, or non-moisturizing soap and water and a soft cloth to gently wipe away dulling dirt and oils.
Avoid metal polishes or scrubbing soaps, because these contain abrasives which may scrub away the sub-micron thick color layer.