The apps this week are among the most impressive apps I’ve seen for iPhone.

GPush ($0.99)

I finally took the dive and bought GPush – an app which sends Push Notifications the second you receive a new message to your Gmail. First of all, it works. Second of all, you probably need it.

I have a lot of email accounts, including Yahoo, MobileMe and Gmail. I use each of them differently. MobileMe is the address I give out to business contacts, Yahoo is the one I use to sign up for anything and Gmail handles everything else, including the bulk of my personal emails.

When I installed GPush and received my first Push Gmail message, something dawned on me. I’ve been using my Gmail account far less than I should specifically because the messages are delayed by 15 minutes. Yahoo and MobileMe messages are pushed to your iPhone instantly while Gmail is checked every 15 minutes. Hence the need for GPush.

While Google is generally ahead of the curve on implementing must-have features the company has been way behind on this one.

Gmail is easily the best web-based free email service and I’d cancel MobileMe pretty quickly if I could just get a better account name. Stupid Ian Hamiltons, you took all the good account names. It’s ok though – there can be only one www.facebook.com/ianhamilton and I am he. Muhahahahahahaha.

Way off topic. I apologize. Back to point.

I hadn’t really paid attention, but in recent months I’ve been having more and more emails sent to Yahoo account rather than Gmail because of that 15 minute delay.

GPush has beautifully solved that problem. It might be better if Gmail had Push, and, knowing Google’s tendency to drop new features whenever it suits them, it could drop any day. For now, this really does work and it’s nice being able to see who is sending you a message without having to open up the Mail app.

Sudoku Grab ($0.99)

One of those awesome wow apps only possible on iPhone. Take a picture of any sudoku puzzle and the app uses photo recognition to identify the numbers automatically. So you can take the puzzle found in your favorite newspaper, book or magazine and put it in your pocket.

You can choose to solve it yourself or just let the iPhone solve it for you.

Check it out in action:

Now, who thinks someone can do the same for crossword puzzles?

Kayak (Free)

The best hidden gem I’ve found yet, I think, because it literally saved me hundreds of dollars. I was looking for a hotel to stay at for several days and couldn’t find anything under $59/night using the mobile version of hotels.com. I spent two minutes in Kayak and found three hotels to choose from at the dirt-cheap (by southern California standards) prices of $33, $35 and $38/night. I opted for the $38/night hotel becase it was closest to where I wanted to be.

When I arrived at the hotel, the guy at the front desk paused for a second while writing my booking rate onto the receipt. Not even he really understood how I got that low a rate.

I wasn’t expecting much for the price, but the hotel had a clean pool and free wireless internet while the room sported a refrigerator, microwave, air conditioning, HBO and an ironing board.

Kayak works, like the Web site of the same name, by pulling the prices from other hotel searching sites and ranking them the way you want. Looking for class? Order the hotels by quality. Looking for somewhere close? Order them by distance to your current location. Looking for cheap? Of course you’re looking for cheap, so make sure to order it from cheap to expensive.

Kayak also does flight searches, but I haven’t actually tested it yet. Though if it works anything like the hotel search, you’ll be saving a lot of dime thanks to Kayak.

There are some complaints about the app crashing in the reviews, but I didn’t experience any crashes in testing. Kayak is nearing the top of the Travel apps, but unless you’re planning a trip in the near future, you probably haven’t noticed it. Now that you do know about it, make sure to download this one and install it on your phone until the time is right.

Simplify Music 2 ($5.99)

If you’re a music fanatic there’s no way you can fit your entire music library on your iPhone. Instead, use Simplify Music 2 to stream it.

The app streams the music collection on your computer no matter the connection. Between apps, videos and photos, space can fill up fast on your iPhone and Simplify Music 2 is here to help.

It works great.

There’s a catch though. The company making this app, Simplify Media, annoyed a lot people when it became one of the few companies not to offer massive upgrades to its app for free. Instead, they released Simplify Music 2 as a completely separate app.

Though incredibly useful, there’s still an important feature missing from Simplify Music 2. You can’t play the playlists from your computer system. You can create playlists inside the app, but that’s tedious compared to the simplicity of importing your playlists from the computer.

If Simplify Music 3 is released as a separate app and supports this basic playlist functionality and they don’t import it into Simplify Music 2, I’ll be the first to organize a boycott.