Utah may not be the startplace of challenges. I am not sure if there was a startplace. However there sure are a lot here. I thought I would list some of the different ones. In particular the ones that may get listed today. If they are questionable, I left them off the list. Hopefully they will give you some ideas. There are about 300 in Utah right now. Though not all unique, there is a lot of variation and a lot of ideas. They are just a sampling. So enjoy.
Utah's Oldest Challenge
GCREMT 1000 Cache Finds Cache Challenge by Dorkteam6 - This the oldest challenge that I know of. Though I am sure there are others nationally, this is the oldest in Utah. Placed in November 2005 it was simple and straightforward. Find 1000 caches before logging.
GCYXXZ Utah DeLorme Challenge - Delorme challenges are pretty common. Find a cache for each page of the Delorme Mapbook. Some areas can do it in a day. In utah expect many days to get those obscure little corners.
GC3AVA9 Utah's Well Rounded Cacher (Fizzy Challenge) - Find a cache for every square in the Difficulty Terrain Grid.
GC1CR3H The GC Icon Challenge - Find one cache from each of the regular icons (excluding the rare ones)
GC1Q51K Jasmer Challenge III - Utah - This is a challenge to find a cache for every month since the start of geocaching. The later months are pretty easy. The earlier ones can mean many miles of driving to get the caches.
GC1YEJG Cache Every Date Challenge - 100% - Find a cache for every day of the year.
GC3993M 7 Icons in a Day Challenge - Find 7 icons in a day.
GC15Y83 An Alphabet Soup Challenge for Utah - Find a cache that starts with every letter of the alphabet.
GC1D60W Alphabet Cities Challenge - UT - Find a cache in a city that starts with every letter of the alphabet.
GC2AB1K Utah Color Cache Challenge - Find 30 caches that have a color name in the title.
GC2B969 Eeny, Minnie, Miny, Moe - A Name Challenge - find 150 caches with peoples names in the title.
GC1PRHH Challenge of the Century: 100 finds in ONE day - Find 100+ caches in a single day. This used to be very hard, not so much any more, but still can take some planning.
GC2FE5W Challenge of the Century: Event Caches - Find 100 event caches. There are also other caches for many of the other cache types.
GC42R8P Earthcache Mica Discovery Challenge - Find 100 earthcaches
GC2ND3G Twenty Two Kay Challenge - Find 22,000 geocaches
GC30194 Streak Milestone Challenge - 300 - Find caches every day for 300 days.
GC1X2WC --Ancient Caches of Utah Challenge-- - Find one of the two oldest caches from each cache type in the state.
GC34EP7 Oldest Active Challenge - Find the oldest active caches in five states.
GC1XRME Oldest in Provo Challenge - Find the 10 oldest active caches in the city.
GC1EMWD Elevation Bands Challenge - This one is finding a cache in every 1000 foot altitude band. 0-1000, 1000-2000, up to the final level that is 10,000+
GC1Z0PR Lonely Cache Challenge - This particular one has you find lonely cache (those that have not been found in some time). Then some specific info on tallying those to a qualification point.
GC2936D 4 States in a Day Challenge - Find four caches in a day in different states. Could be tricky in the western US.
GC27KRZ 3 States, Same Name Challenge - Find caches in three different states, but are in towns that have the same name.
GC2G58M Challenge of the Century: 100 Unique Challenges - Find at least 100 challeges.
GC2H41Q Salt Lake County Thin Air challenge - Find a number of caches that are over 9700 feet in altitude, that total over 10,000 feet in altitude
GC2NK18 Souvenir Challenge - Earn at least 10 souvenirs.
GC2P4WW Waymarking History Challenge - Find 100 history based waymarks.
GC2PX82 Triple Double Challenge - Find 10 caches of three different cache types in a day.
GC3019F Finds by Placed Date Challenge Cache - Find a cache that was placed on every day of the year.
GC38A9P 4x4 Challenge - Find 10 caches with certain attributes.