A couple of things to check before you pull the lower unit.
1. Disconnect the shift cable at the engine and make sure that when you move the shifter into reverse, that the cable moves as it should.
2. Grab the end of the cable at the engine end and make sure that it does not pull out of its sheath. The cable may be broken....although forward is normally affected when that happens.
3. With the engine turned off.....turn the propeller clockwise with one hand or foot while moving the shift lever to the rear. See if the prop locks up/engages. If it does, then it may not be in the lower unit.
4. Check your shift arm....#13. There is a safety recall on early models of the 150 for the shift arm....definitely check it if your serial number is in the affected range
http://cdn.powerequipment.honda.com/marine/pdf/recalls/W-BF135-BF150-recall-notice.pdf
5. If everything still takes you to the lower unit, drain the gear lube and check it for metal shavings, water, no gear, etc.
6. Once you take the lower unit off, you can try to shift it by hand again. The manual shows how to do it.
7. If you have to take the lower unit apart, follow the manual. You have to remove the water pump first, then the shift shaft. Only then can you pull out the prop shaft holder. Definitely inspect the clutchdog and the reverse gear.
Also, check the shifter pin #2
http://www.boats.net/parts/search/H...50AK2 LA/PROPELLER SHAFT PROPELLER/parts.html
If it is fractured from an impact, it may still partially work. If fractured, then tend to work ok in forward, but not so well in reverse.
Hope you find something simple.
Mike