Very tough question...I have dozens of rifles...here's my favorites judged on biased and emotional rationale versus any specific objective criteria.
1. M1 Garand -- because I'm a red-blooded American who grew up in the 60's watching WWII movies. And because it is a lot of fun to shoot as well. Not the ultimate battle rifle, but one that is full of history
2. FN-FAL -- this is the rifle I reach for the most from the safe because it is ergonomic, powerful, reliable and good looking. 90 countries can't be wrong.
3. 1874 Sharps -- drop dead gorgeous, extremely accurate and came at a pivotal time in our nation's development. Plus, Quigley can't be wrong, can he?
4. Finnish M39 -- I've been enjoying reading and thinking about the Winter War and the Continuation War recently. The M39 represents what a small, determined populace can do against impossible odds based on the independence of it's people...and marksmanship. Everything the Mosin-Nagant wanted to be...but wasn't sophisticated enough to think of.
5. AR15 -- I used to "hate" AR15s until I actually owned one. Now I have 7. They are infinitely customizable, sufficiently powerful, handy, ergonomic and a lot of fun. This one is set up just like I want it.
Honorable mention (because I was too chicken$#!% to choose just 5)
1. M1A/M14 -- for the same reasons I like the Garand...with 20 rounds instead of 8. This one is extremely accurate.
2. Tikka T3 -- not the prettiest or most refined but I call this one my "hammer of Thor". Has never failed to anchor an animal on the spot. I would be lying if I said I didn't like it.
3. Winchester 1892 -- super handy, fast firing, powerful enough, accurate enough. The "assault rifle" of it's day...and still pretty formidable in the right hands. This one is a Rossi in .45 Colt. Wouldn't feel undergunned with one.
4. Swedish M96 -- elegant, from another time of craftsmanship. Crazy accurate with an wonderful old cartridge...I love the 6.5x55mm.
5. Steyr AUG -- surprised myself including this...especially over the M1903. But I really appreciate the forward thinking of the design and the incredible compactness of the machine. Bullpups have lots of flaws, but also some advantages that are unavoidable.