USMCmech is correct that logbooks are not required, but it's not so simple. The FAA doesn't require a logbook per se, but requires maintenance records for each airframe, powerplant, propeller, appliance, etc. These may be kept in separate dedicated books, in a shoebox crumpled together, or any other number of systems. Keeping separate logs for major items such as the airframe, powerplant(s), and propeller(s) is common and accepted practice, and a very good idea.
Whatever the maintenance records are that you have, you need to bring them. If you have engine logs and propeller logs, then you betcha, they absolutely do need to be there for the annual inspection. If you are using a logbook, a file folder, a shoebox, or any other system, it needs to be there. The mechanic performing the inspection (your IA) needs those logs to verify that all applicable maintenance done on them, including required inspections and AD's, has been properly logged and signed off. He needs to be able to verify component times, and is almost certainly going to want to know the history of the aircraft.
Some mechanics don't bother putting a signature in the airframe logs or the propeller logs covering an annual inspection. They can legally do this; the aircaft is being inspected as a whole. However, in cases where logs are separated into component logs (separate engine and prop logs), I believ in including notations in each log regarding the extent of the work done and any inspections performed. If an annual or progressive inspection is performed, I note it in each logbook.
The matter is sometimes hotly contested. Some mechanics do, some don't. Some feel that becase signing off an aircraft as airworthy and approving it to return to service "buys the past," they're extending their liability farther by providing additional endorsements for the powerplant and propellers...when those components eventually get separated or sold off for overhaul, that signature goes with them and could conceivably come back to haunt an inspector. After all, when you perform an inspection, you take responsibility for everything that's been done to it in the past, including any inspections, work, modifications, changes, routine maintenance, etc...you make no statement to the future, but as an inspector, you buy the past...you put your signature at the top of the heap and take on an enormous responsibility that covers everything in that aircraft's history as your own...and you singly hold that responsibility until someone else performs that inspection and signs it off next. Therefore, some mechanics don't like to extend themselves more than the need to.
Of course, providing a log endorsement that the aircraft is airworthy does this anyway...additional signatures don't take on any more responsibility...the inspector has already accepted it all.
When performing the inspection, an important aspect of the overall process is knowing that the aircraft is in compliance with all approved data. This includes airworthiness directives, and ensuring that all prior repairs have been documented properly.
In order to do this, the maintenance records are required, and if you have maintenance records for the powerplant and the propeller, then you need those present to properly perform the inspection. The mechanic may or may not elect to endorse them, but he definitely needs them.
If all the record were combined in one, and that's perfectly legal (but not practical), then one endorsement for the aircraft record woud suffice. However, very likely the engine that's in that aircraft will eventually be sold or changed out, and the logs will go with it. Recording the vital statistics at the time of the inspection such as static cylinder leakage test values, results of a spectrometric oil analysis, etc, should be made and kept in the engine log, along with details of any service done during the annual and post-annual work. Including a statement that it was done as part of an annual inspection provides a clear and concise reason for what was done, and helps tie the logs together. Same goes for the propeller.
An aircraft needs an annual inspection. An engine by itself does not. But when it's attached to te airplane, it's part and parcel with the rest of the aircraft, and does need to be included in the annual inspection and hundred hour (if applicable). Bring the logs. Your mech should ask for them...if he doesn't, get another mechanic.