There are three types of accommodation to consider when visiting Venice: hotels, apartments and hostels. There are also two main locations to consider: Venezia (the historic City centre that everyone considers to be "Venice") and the Mestre, a suburban area based on the mainland separated from Venezia by the Causeway. I would suggest that if you can stay in Venezia itself this is the best option (atmosphere...) but it is generally more expensive than the Mestre. The hotels in the Mestre also tend to be more modern but you need to bear in mind that you will need to take a bus or taxi each way to visit the historic City centre. 
I am going to concentrate on the hotels in Venezia because, to be honest, I am not that familiar with those in the Mestre. 
As you would expect, prices vary according to season and demand with the most expensive times being high season (Easter through September) and at Carnival. In terms of price, it is worth doing your homework because the various price comparison sites occasionally throw up some really good bargains. Occasionally, but not often. I try and stay in 3*-4* hotels and expect to pay between €120-130 per night in March. Prices can double or even triple at more popular times. Again, homework is the key. I list below some of the hotels I have stayed in or have received good reviews and comments from friends. I am not, however, endorsing any of them because standards rise and fall and because I haven't stayed in them all. 
Just a couple of notes: if you are used to Las Vegas style hotel rooms you will not find them in Venice. Rooms tend to be small although well furnished (3* and above) in the ornate Italian style. Bathrooms can also be a bit Lilliputian on occasions. Breakfast is generally continental and, unless included in the price, you'll generally get a better deal in a cafe. Oh, and air conditioning isn't a given so if you need it, check with the hotel or its website. 
Ok. Some of the hotels I know or know about (a star indicates that I have stayed there and found to be good, but see my comments above about variable standards): 
4 Star **** 
Doudo Palace Calle Minelli, San Marco 1887* 
At the time of writing, my hotel of choice. This is a clean comfortable hotel with modern interior furnishings. It has delightful, helpful and friendly staff and relatively spacious rooms by Venetian standards. The hotel is very central - just 5 minutes walk from St Mark's Square and 10 minutes (if you know your way!) to the Rialto - but is situated in a very quiet location just a few steps from the Fenice Theatre. 
Breakfast is continental (ham, cheese, croissants, rolls, fresh fruit, cereal, cake, jam etc) with attentive and fast service in the tea and coffee department. Breakfast is usually included in the price but you can order cooked egg dishes for a small supplement. 
Comfortable beds, clean modern bathrooms, and television that works (although English service is restricted to BBC World and CNN). 
Hotel Kette San Marco, 2053* 
All of the comments for the Duodo Palace apply here. The exception being that it is generally more expensive, the rooms are on the smaller side and the decoration a little more ornate and traditional. Very central and close to the Fenice Theatre. 
Rialto Hotel San Marco 5149* 
This hotel is situated right next to the famous Ponte de Rialto. As such, it can be a little noisy (very noisy at Carnival!). Attentive reception staff but really small rooms and it also caters for the group tourist trade and all that entails. That may sound negative but actually it is not a bad hotel at all and its central location means that it is easy to get to on the fast No 2 vaporetto. 
Breakfast is a good continental selection but the restaurant was rather crowded when I stayed although that was at a particularly busy point during Carnival. It is a perfectly good hotel to stay at albeit cramped. It boasts rooms with a view of the Grand Canal but I suspect you pay rather highly to get one. Would I stay again? Yes. 
Hotel San Cassiano Santa Croce,2232 
3 Star *** 
Hotel Malibran Cannaregio 5864* 
This is the home of one of my favourite restaurants (see the Eating section) and I have also stayed here a couple of times. The accommodation consists of two locations - the main hotel and an Annexe. The room I had in the Annexe was perfectly fine with a reasonable amount of space and a clean modern bathroom and a comfortable bed.  
The second room was in the main hotel where the room was much smaller, rather dark and with a small bathroom. On balance I would only take accommodation here if you can get an Annexe Room. Breakfast is continental with food served in the main restaurant. As with my comments regarding the restaurant, one of the main attractions is the friendly and helpful staff. 
The hotel is situated close to the Rialto Bridge but in a small, quiet courtyard. Reasonably priced out of main season. 
This is a pretty good option for larger families or groups as the cost per room comes tumbling down. Rates still vary with season but are pretty good value. There are a huge number of agencies offering apartments and I have none, particularly, to point you towards. I have used apartments twice and price and location have been my guiding factors. 
There are some peculiarities about renting apartments in Venice some of which are a bit annoying. The first is that agents/owners like to be paid in cash. In some cases, the owner or agent will meet you at the vaporetto stop and walk you to the apartment and then go through paperwork and keys. This is usually a simple and easy arrangement. Others, however, work through a rental office based at Piazzale Roma that has limited opening hours at weekends. With this arrangement, if you arrive out-of-hours, you go to the office, enter a keycode take your key and then find your apartment on your own. The following day you have to go back to settle up. Frankly, it is a pain in the gluteus maximus!  
The other factor you have to consider is that you will be expected to vacate the apartment at around 10am. If your flight isn't until the evening, what do you do with your luggage? Some owners will make an arrangement but not all. In the latter case you either drag your bags around all day or take them to left luggage. The problem is the only left luggage offices are at the railway station and Piazzale Roma at the North end of the City. And, of course, you then have to pick them up again on your way out to the airport. This all sounds very negative, but you do need to be aware. Don't be put off as apartments are a good option in the right circumstances. 

NOTE: There are rumours that the City Council may be putting restrictions on short-term lets, so be aware and do your homework.
I have no direct experience of hostels in Venice. There are, however, a very large number of websites aimed at the budget traveller that contain details of available hostels together with reviews