Garfield gets very sentimental around Christmas. In one strip, he was asked what he wants for Christmas, and responds by saying that he wants a "second helping" of the food, shelter and love he already has.
When Jon and Liz finally get together. "And they lived happily ever after."
And earlier, when Jon stumbles in on Liz's date with some other guy. The other guy asks something along the lines of "What, do you like this idiot?" and, not missing a beat, Liz says "As a matter of fact, I do".
This. A more subtle example, but considering Jon's life, it's quite a heavy-hitter.
The first time Jon's Grandma came to visit. Garfield is affectionate to her all week, and is sad to see her go.
This strip is relatively minor, but it still shows that Garfield really does have a sentimental side.
The last comic of the Thirtieth Anniversary book. In it Garfield gushes over his teddy bear (which is nothing new) but Davis' note at the bottom talks about his first assistant Valette Green who passed away some time ago. If you look carefully at the last panel of the strip you can see her in name spelled out in the stars.
Another Christmas strip, which could be seen as an allegory of Jon's life:
Jon: One thing I'll never understand, Garfield. In spite of all the chaos, the ugly tree, and the old decorations... everything turns out perfectly.