Is your mare ATA or Canadian Trakehner approved? That might make a difference to which stallion you choose if you are concerned about registration.
What are her bloodlines?
What is your mare's temperament like? What is your breeding goal ie. upper level horse or ammy friendly? My best friend/neighbour has an Asher baby who is really lovely but HOT. I know Asher himself is quiet and this may be more to do with the mare, but if your mare is not approved with either Trakehner registry and you are looking to produce an easy temperament, I would consider looking into a breed other than Trakehner as they are known (and indeed bred) to be "hotter" than most other warmblood breeds because of the prevalence of Arab and TB blood.
With a few exceptions, Trakehners are not known for jumping; the breed has been established for dressage and eventing in general. If you are interested in producing a hunter, Asher might be a good choice; however, if you are interested in producing a jumper, I would look at a stallion from one of the breeds known to produce jumpers, like Holsteiner, KWPN or select Hanoverians in their jumper breeding program.
If you don't mind going the frozen route, consider Grafenstolz. He's about as proven as it gets performance-wise, and is a very popular event/dressage sire in the UK. Competed Prix St. George dressage, 3* eventing and puissance jumping to almost 7 feet! http://www.thestallioncompany.com/stallion_detail.php?stallion=2007025
He is available from Judy Yancey in FL at yancey-farms.com
Hirtentanz is a fantastic up and coming Trakehner jumper stallion, approved Holsteiner which is very rare for a Trakehner. Also only available frozen.http://americantrakehner.com/Stallions/Hirtentanz.asp
Consider Horalas as well; he was a Grand Prix jumper with Hap Hansen.http://americantrakehner.com/Stallions/Horalas.asp
Special Memories, a son of Abdullah, has a pretty impressive record at Grand Prix, having competed in several World Cup qualifiers. He also evented Prelim. Not too shabby.http://americantrakehner.com/Stallions/SpecialMemories.asp
Tzigane also has an impressive jumping record; impressive enough that he has been imported back to Germany.http://americantrakehner.com/Stallions/Tzigane.asp
Titulus is moving his way up the ranks of the jumper world; I believe he is competing at Level 7. He is actually Canadian-owned but is currently standing in the U.S.http://americantrakehner.com/Stallions/Titulus.asp
If you're thinking more of an amateur jumper and wouldn't mind incorporating eventing lines, Darren Chiachia has two really nice up and coming imported event stallions worth considering:http://americantrakehner.com/Stallions/Ballzauber.asphttp://americantrakehner.com/Stallions/Zauberruf.asp
There are some other great Trakehner event stallions available: check out the Valhalla stallions:
Again, though, if it is a jumper you are looking to produce, consider having your mare approved with another registry (eg. Canadian Warmblood, RPSI) and pick a more jumper-oriented breed. Check out holsteiner.com for the AHHA stallion roster. The Holsteiner stallion service auction is still going on until Feb. 14, so there are some deals to be had on great Holsteiner jumper stallions!