It seems like he's trying to be the next Adam Sandler, but his sketches generally lack the emotional nuance that made Sandler so good.
I don't watch SNL anymore (if there's a good sketch I just watch it on Hulu), so I don't know how often he's featured on the rest of the show or if he's funny in regular sketches, but I think his music and video parodies are pretty good. I never even bothered to watch his movie because it looked awful. Videos: I'm on a Boat (Explicit) which is with his "band" The Lonely Island (and T-Pain) and makes fun of the Akon video I'm so Paid along with similar rap videos. Jizz in my Pants by The Lonely Island. Hero Song, an SNL Digital Short. This one features Samberg and Justin Timberlake dancing in the Beyonce video for All the Single Ladies wearing the tights the girls wore in the video. Iran so Far Away an SNL Digital Short love song to Mahmoud Ahmadinejad featuring Adam Levine from Maroon 5. Lazy Sunday, probably his most famous Digital Short. And Dick in a Box (Uncensored), again with Justin Timberlake.
Arrogant Annoyance. He has done some funny stuff, as Locutus mentions above, but he and Dave Foley top my "smirking-celebrities-I-want-to-punch-in-the-face" list.
I'm on a Boat is the funniest thing I've seen in a long time, so I think he's well on his way to being somebody.
That's my favorite one, and it's actually a pretty catchy tune on its own. T-Pain makes it perfect, though.
His Digital Shorts are absolutely hilarious, but in the regular sketches he's pretty forgettable. I kinda liked Hot Rod, though. So I say somewhere in between.
Loved Hot Rod - I'm in a minority with that though I get the impression he's like Will Ferrell Mk II, but I'm starting to go off that style of comedy in my old age, so I've voted for "somewhere in between".
Besides the ones mentioned above, there's: Just 2 Guys (Only appears briefly, but all 3 guys wrote this show) The Awesometown Theme Business Meeting (Another short appearance, but it's a digital short, which he writes for) Lazer Cats (This is 2 of 4) There are even more examples, but how many do you need? Yes, the guy is funny.
I was trying to hold my opinion until everyone else had said their piece. Personally, I find it hard enough to laugh at anything that happens on SNL. Bill Hader and Kristen Wiig are the only actually funny ones on there. Samberg's giggly 'look at me, I'm so funny' style makes me want to watch less.
I don't know where I fall on the Samberg fence but he is interesting because he brings a real 21st Century plugged-in online sensibility to the show. And I'm not 100% sure if he was responsible for it but if he did the Natalie Portman rap I'd lean toward comic genius.